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Leibniz-Informationszentrum WirtschaftLeibniz Information Centre for Economics
Becker, Christoph; Wystup, Uwe
Working Paper
On the cost of delayed currency fixing
announcements
CPQF Working Paper Series, No. 3
Provided in cooperation with:
Frankfurt School of Finance and Management
Suggested citation: Becker, Christoph; Wystup, Uwe (2005) : On the cost of delayed currency fixing announcements, CPQF Working Paper Series, No. 3, http://hdl.handle.net/10419/40178
No. 3
On the Cost of Delayed Currency Fixing
Announcements
Christoph Becker
Uwe Wystup
Author: Christoph Becker Prof. Dr. Uwe Wystup
MathFinance AG HfB – Business School of Germany Finance & Management
http://www.mathfinance.de Frankfurt/Main Germany
June 2005
Publisher: HfB - Business School of Finance & Management
Phone: +49 (0) 69 154 008-0 § Fax: +49 (0) 69 154 008-728 Sonnemannstr. 9-11 § D-60314 Frankfurt/M. § Germany
Abstract. In Foreign Exchange Markets vanilla and barrier options are traded frequently. The market standard is a cutoff time of 10:00 a.m. in New York for the strike of vanillas and a knock-out event based on a continuously observed barrier in the inter bank market. However, many clients, particularly from Italy, prefer the cutoff and knock-out event to be based on the fixing published by the European Central Bank on the Reuters Page ECB37. These barrier options are called discretely monitored barrier options. While these options can be priced in several models by various techniques, the ECB source of the fixing causes two problems. First of all, it is not tradable, and secondly it is published with a delay of about 10 - 20 minutes. We examine here the effect of these problems on the hedge of those options and consequently suggest a cost based on the additional uncertainty encountered.
Keywords: Exotic Options, Currency Fixings
JEL classification: C15, G12
Acknowledgments. We would like to thank Michael Braun, Ansua Dutta-Wystup, Thomas Heidorn, Wolfgang Schmidt and Dagmar Wicht for their help and comments.
Contents
1 Introduction 3
1.1 The Currency Fixing of the European Central Bank . . . 3
1.2 Model and Payoff . . . 4
1.3 Analysis Procedure . . . 4
2 Error Estimation 5
2.1 European Style up-and-out Call. . . 5
2.2 Discretely Monitored up-and-out Call . . . 6
2.3 Calculating the Delta-Hedge Quantity . . . 7
3 Analysis of EUR-USD 7 4 Conclusion 10 5 Appendix 11 5.1 Analysis of USD-CHF . . . 11 5.2 Analysis of USD-JPY . . . 13 5.3 Analysis of EUR-GBP . . . 15
1
Introduction
1.1
The Currency Fixing of the European Central Bank
The European Central Bank (ECB) sets currency fixings every working day in Frankfurt at 2:15 p.m. Frankfurt time. The actual procedure of this fixing is done by observing the spot rates in the inter bank market, in which the ECB also participates. Traders of the ECB in various locations get together to decide on how to set the fixing. The quantity quoted is not a bid price or an offer price the ECB or anybody else necessarily trades at, but is rather used for statistical and official means, for instance tax computation or economic research. An example of the ECB37 REUTERS screen is presented in Figure1.
Figure 1: Reuters screen ECB37 of 21 February 2005 showing the fixings of all cur-rencies against EUR
Corporate treasures often prefer an independent source for currency exchange rates that provides a reference rate for their underlying under consideration. This way they are not bound to their own bank that might move the quoted cut-off rate in favor of their own position. The key features to stress are the following.
1. The ECB fixing is nottradable.
In this paper we analyze the impact on the value for the short position of a discretely monitored reverse knock-out, as the problems mentioned above impose additional uncertainty when it comes to determining a proper hedge. Most of the hedging error is expected in the case of jumps in the payoff of the option, which is why we restrict ourselves to the liquidly traded up-and-out call option. The currency-pairs under consideration are EUR-USD, USD-JPY, USD-CHF and EUR-GBP.
1.2
Model and Payoff
To model the exchange rate we choose a geometric Brownian motion,
dSt=St[(rd−rf)dt+σ dWt], (1) under the risk-neutral measure. As usual,rd denotes the domestic interest rate,
rf the foreign interest rate, σthe volatility. These parameters are assumed to be constant in this paper. For contract parameters maturity in years T, strike
K and knock-out barrierB, fixing schedule 0 =t0 < t1 < t2. . . , tn = T, the payoffs for the vanilla and for a discretely monitored up-and-out barrier option under consideration are
V(FT, T) = (φ(FT −K))+, (2)
V(F, T) = (φ(FT −K))+II{max(Ft0,...,Ftn)<B}, (3)
where Ft denotes the fixing of the underlying exchange rate at time t, II the indicator function andφa put-call indicator taking the value +1 for a call and
−1 for a put. Of course,Ftis usually close toSt, the spot at timet, but it may differ as well. We start with payoffs
V(ST, T) = (φ(ST−K))+, (4)
V(S, T) = (φ(ST−K))+II{max(St0,...,Stn)<B}, (5)
whose values are explicitly known in the Black-Scholes model. In this model, the values are calledtheoretical value (TV).
1.3
Analysis Procedure
1. We simulate the spot process with a Monte Carlo simulation using an Euler-discretization. Furthermore, we use a Mersenne Twister pseudo random number generator by Takuji Nishimura and Makoto Matsumoto [5] and a library to compute the inverse of the normal cumulative distribution function written by Barry W. Brown et al. [2].
2. We model the ECB-fixingFtby
Ft=St+ϕ, ϕ∈ N(µ, σ), (6) whereµandσare estimated from historic data. Note thatFtdenotes the ECB-fixing at timet, which is nonetheless only announced 10 - 20 minutes later. We denote this time delay by ∆ECB(T). This means that we model the error, i.e. the difference of fixing and traded spot, as a normally distributed random variable. The estimated values for the mean and the
standard-deviation of the quantity Spot - ECB Fixing from historic time series are listed in Table1. For the cross rates, where EUR is not one of the currencies, we take the respective ratios of fixings against EUR, e.g. for the USD/JPY fixing we divide the EUR/JPY fixing by the EUR/USD fixing, which is also common market practise in trade confirmations.
Currency pair Expected value Standard deviation Time horizon EUR / USD -3.125E-6 0.0001264 23.6 - 08.8.04 USD / YEN -4.883E-3 0.0134583 22.6 - 26.8.04 USD / CHF -1.424E-5 0.0001677 11.5 - 26.8.04 EUR / GBP -1.33E-5 0.00009017 04.5 - 26.8.04
Table 1: Estimated values for mean and standard-deviations of the quantity Spot - ECB-fixing from historic time series. The time series were provided by Commerzbank AG
3. We evaluate the payoffs for barrier options for each path and run the simulations with the appropriate delta hedge quantities to hold. Then we compute for each path the error encountered due the fixing being different from the spot, and then average over all paths.
4. We do this for various currency pairs, parameter scenarios, varying the rates, volatilities, maturities, barriers and strikes. We expect a significant impact particularly for reverse knock-out barrier options due to the jump of the payoff and hence the large delta hedge quantity.
2
Error Estimation
Note that since we expect the resulting errors to be fairly small, we introduce a bid/offer-spreadδfor the spot, which is of the size of 2 basis points in the inter bank market. We consider the following options in detail.
2.1
European Style up-and-out Call
To determine the possible hedging error we propose the following to be appro-priate. Note that the error is measured for a nominal of 1 unit of the underlying. We consider three cases.
1. Let ST ≤K. In this case, the seller who is short the option decides not to hedge as the option is probably out of the money, i.e. delta = 0. If the option turns out to be in the money, i.e. FT > K, the holder of the short position faces a P&L of K−(S(T + ∆ECB(T)) +δ) (units of the base currency).
2. Let ST > K and ST < B. Hence, one assumes that the option is in the money and delta is 1. If now FT ≤ K or FT ≥ B, there is a P&L of
3. LetST ≥BandFT < B. Here we have a P&L ofK−(S(T+∆ECB(T))+
δ). Note that other than in the first case, this P&L is of orderK−Bdue to the jump in the payoff.
2.2
Discretely Monitored up-and-out Call
We consider a time to maturity of one year with 250 knock-out-events, i.e., the possible knock out occurs every working day at 2:15 p.m. Frankfurt time, when the ECB fixes the reference rate of the underlying currency pair. We propose the following error determination to be appropriate. First of all, we adopt the procedure above for the maturity time. In addition, we consider every knock-out-event and examine the following cases.
1. LetSt< BandFt≥B. At timetthe trader holds ∆(St) shares of stock in the delta hedge. He does not unwind the hedge at timet, as the spot is below the barrier. Only after the fixing announcement, it turns out that the hedge needs to be unwound, so he does this with delay and encounters a P&L of
∆(St)·(St+∆ECB(T)−St), (7)
where ∆(St) denotes the theoretical delta of the option under consider-ation, if the spot is at St. To see this, it is important to note, that the theoretical delta is negative if the underlying is near the barrierB. In this way, the seller of the option has been short the underlying at time t and must buy it int+ ∆ECB(T) minutes to close out the hedge. Therefore, he makes profit if the underlying is cheaper int+∆ECB(T), which is reflected in our formula. We shall elaborate later how to compute the theoretical delta, but we would like to point out that whenever we need a spot price at timet to calculate such a delta or to compute the value of a hedge, we refer toSas the tradable instrument instead of the contractually specified underlying F in order to account for the ECB fixing being non-tradable. 2. Let St ≥ B and Ft < B. Here the seller of the option closed out the
hedge at timet, though she shouldn’t have done so, and int+ ∆ECB(T) she needs to build a new hedge. Note again that the theoretical delta is negative. This means that at timetthe seller bought the underlying with the according theoretical delta-quantity, and in t+ ∆ECB(T) she goes short the underlying with the appropriate new delta-quantity. The profit and loss (P&L) is calculated via
P&L = ∆(St)·(St+δ)−∆(St+∆ECB(T))·St+∆ECB(T) (8)
The other cases do not lead to errors due to an unexpected fixing announcement. Of course, delta hedging an option in the Black-Scholes model can lead to errors, because of hedge adjustments at discrete times and and because of model risk in general, see, e.g. [1].
2.3
Calculating the Delta-Hedge Quantity
The valuation of continuously monitored barrier options has been treated, e.g., in [3]. In order to compute the theoretical delta for the discretely monitored up-and-out call, for which no closed-form solution is known, in acceptable time and precision, we refer to an approximation proposed by Per H¨orfelt in [4], which works in the following way. Assume the value of the spot is observed at times
iT /n,i= 0, . . . , n, and the payoff of the discretely monitored up-and-out call is given by Equation (5). We define the value and abbreviations
θ± ∆ = rd−rf±σ 2/2 σ √ T , (9) c =∆ ln(K/S0) σ√T , (10) d =∆ ln(B/S0) σ√T , (11) β =∆ −ζ(1/2)/p(2π)≈0.5826, (12) whereζ denotes the Riemann zeta function. We define the function
F+(a, b;θ) ∆
=N(a−θ)−e2bθN(a−2b−θ) (13) and obtain for the value of the discretely monitored up-and-out call
V(S0,0) ≈ S0e−rfT F+(d, d+β/ √ n;θ+)−F+(c, d+β/ √ n;θ+) (14) −Ke−rdTF +(d, d+β/ √ n;θ−)−F+(c, d+β/ √ n;θ−).
Using this approximation for the value, we take a finite difference approach for the computation of the theoretical delta,
∆ =VS(S, t)≈
V(S+, t)−V(S−, t)
2 . (15)
3
Analysis of EUR-USD
Considering the simulations for a maturityT of one year, huge hedging errors can obviously only occur near the barrier. The influence of the strike is com-paratively small, as we discussed in the error determination procedure above. In this way we chose the values listed in Table 2 to remain constant and only to vary the barrier.
Using Monte Carlo simulations with one million paths we show the averageof the profit and loss with 99.9% confidence bands and how the probability of a mishedge depends on the position of the barrier in Figure 2. It appears that the additional costs for the short position are negligible. We also learn that the mishedge is larger for a barrier in a typical traded distance from the spot, i.e. not too close and not too far.
In Figure3we plot the barrier against the ratio Hedging Error / TV of the up-and-out call and the ECB-fixing as underlying. This relationship is an important message for the risk-averse trader. For a one-year reverse knock-out call we see an average relative hedge error below 5% of TV if the barrier is at least 4 big
Spot 1.2100
Strike 1.1800
Trading days 250 Domestic interest rate 2.17% (USD) Foreign interest rate 2.27% (EUR) Volatility 10.4% Time to maturity 1 year Notional 1,000,000 EUR
Table 2: EUR-USD testing parameters
Hedge error with 99.9% - confidence interval
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 1.22 1.24 1.26 1.28 1.3 1.32 1.34 1.36 1.38 1.4 1.42 1.44 1.46 barrier error error in USD confidence band Probability of mishedging 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 1.22 1.241.26 1.28 1.3 1.321.34 1.36 1.38 1.4 1.42 1.44 1.46 barrier probability
Figure 2: Additional average hedge costs and probability of a mishedge for the short position of a discretely monitored up-and-out call in EUR-USD
Rel. hedge error with 99.9% bands
-120.00% -100.00% -80.00% -60.00% -40.00% -20.00% 0.00% 1.221.241.261.28 1.31.321.341.361.38 1.41.421.441.46 barrier probability error confidence band
Rel. hedge error with 99.9% bands
-4.50% -4.00% -3.50% -3.00% -2.50% -2.00% -1.50% -1.00% -0.50% 0.00% 1.25 1.27 1.29 1.31 1.33 1.35 1.37 1.39 1.41 1.43 1.45 barrier probability error confidence band
Figure 3: Hedging Error /TV for a discretely monitored up-and-out call in EUR-USD
figures away from the spot. Traders usually ask for a risk premium of 10 basis points.
Finally, we would like to point out that the average loss is not the full story as an average is very sensitive to outliers. Therefore, we present in Figure 4
the distribution of the maximal profits and losses, both in absolute as well as in relative numbers. The actual numbers are presented in Table 3. We have found other parameter scenarios to behave similarly. The crucial quantity is the intrinsic value at the knock-out barrier. The higher this value, the more dangerous the trade. In particular we do not exhibit the results for the vanilla as there is hardly anything to see. Varying rates and volatilities do not yield any noticeably different results.
-300000 -250000 -200000 -150000 -100000 -50000 0 50000 P & L 1.22 1.25 1.28 1.31 1.34 1.37 1.4 1.43 1.46 barrier
Extremal P & L for the short position
max downside error max. upside error
Relative P & L -45000% -40000% -35000% -30000% -25000% -20000% -15000% -10000% -5000% 0% 5000% 1.241.261.281.3 1.321.341.361.381.4 1.421.441.46 barrier P & L in USD
max downside error max upside error
Figure 4: Absolute and relative maximum profit and loss distribution for a discretely monitored up-and-out call in EUR-USD. The upside error is the unexpected gain a trader will face. The downside error is his unexpected loss. On average the loss seems small, but the maximum loss can be extremely high. The effect is particularly dramatic for knock-out calls with a large intrinsic value at the barrier as shown in the left hand side. The right hand side shows the maximum gain and loss relative to the TV. Of course, the further the barrier is away from the spot, the smaller the chance of hedging error occurring. barrier 1.2500 <1k$ <2k$ <3k$ <39k$ <40k$ <41k$ <42k$ <43k$ upside error 951744 20 1 0 0 0 0 0 downside error 48008 54 2 5 59 85 21 1 barrier 1.3000 <1k$ <2k$ <3k$ <89k$ <90k$ <91k$ <92k$ upside error 974340 20 1 0 0 0 0 downside error 25475 43 0 2 40 59 20 barrier 1.4100 <1k$ <2k$ <3k$ <199k$ <200k$ <201k$ <202k$ <203k$ upside error 994854 78 0 0 0 0 0 0 downside error 4825 194 3 1 19 17 8 1
Table 3: EUR-USD distribution of absolute errors in USD. The figures are the number of occurrences out of 1 million. For instance, for the barrier at 1.2500, there are 54 occurrences out of 1 million, where the trader faces a loss between 1000 and 2000 $.
As the analysis of the other currency pairs is of similar nature, we list it in the appendix and continue with the conclusion.
4
Conclusion
We have seen that even though a trader can be in a time interval where he does not know what delta hedge he should hold for an option due to the delay of the fixing announcement, the loss encountered is with probability 99.9% within less than 5% of the TV for usual choices of barriers and strikes and the liquid currency pairs, in which complex barrier options such as a discretely monitored up-and-out call are traded. However, the maximum loss quantity in case of a hedging error can be rather substantial. So in order to take this into account, it appears generally sufficient to charge a maximum of 10% of the TV to cover the potential loss with probability 99.9%. This work shows that the extra premium of 10 basis points per unit of the notional of the underlying, which traders argue is needed when the underlying is the ECB-fixing instead of the spot, is justified and well in line with our results. However, charging 10 basis points extra may be easy to implement, but is not really precise as we have seen, since the error depends heavily on the distance of the barrier from the spot.
Of course the level of complexity of the model can be elaborated further arbi-trarily, but using a geometric Brownian motion and a Monte Carlo simulation appears sufficient. The relative errors are small enough not to pursue any further investigation concerning this problem.
5
Appendix
5.1
Analysis of USD-CHF
We used the market and contract data listed in Table 4. We summarize the results in Table5and Figure5. The results are similar to the analysis of EUR-USD.
Spot 1.2800
Strike 1.2000
Trading days 250 Domestic interest rate 0.91% (CHF) Foreign interest rate 2.17% (USD) Volatility 11.25% Time to maturity 1 year Notional 1,000,000 USD
Table 4: USD-CHF testing parameters
barrier 1.3300 <1k <2k <3k <49k <50k <51k <52k <54k upside error 950902 29 1 0 0 0 0 0 downside error 48846 65 2 9 44 72 28 2 barrier 1.3900 <1k <2k <3k <109k <110k <111k <112k <113k upside error 975939 26 3 0 0 0 0 0 downside error 23847 72 5 4 23 52 27 2 barrier 1.5000 <1k <2k <3k <4k <5k <219k <220k <222k upside error 993544 749 90 2 0 0 0 0 downside error 4523 880 158 12 3 2 12 25
Table 5: USD-CHF distribution of absolute errors in CHF. The figures are the number of occurrences out of 1 million
Hedge error with 99,9% confidence intervall -25 -20 -15 -10 -5 0 1.29 1.31 1.33 1.35 1.37 1.39 1.41 1.43 1.45 1.47 1.49 barrier hedge error in CHF hedge error confidence intervall Probability to mishedge 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 1.29 1.31.311.321.331.341.351.361.371.381.39 1.41.411.421.431.441.451.461.471.481.49 1.5 barrier probability
relative hedge error
-160.00% -140.00% -120.00% -100.00% -80.00% -60.00% -40.00% -20.00% 0.00% 1.29 1.31 1.33 1.35 1.37 1.39 1.41 1.43 1.45 1.47 1.49 barrier error/TV rel error confidence intervall
relative hedge error
-14.00% -12.00% -10.00% -8.00% -6.00% -4.00% -2.00% 0.00% 1.31 1.33 1.35 1.37 1.39 1.41 1.43 1.45 1.47 1.49 barrier error/TV rel error confidence intervall
Extremal P & L for the short position
-250000 -200000 -150000 -100000 -50000 0 50000 1.29 1.31 1.33 1.35 1.37 1.39 1.41 1.43 1.45 1.47 1.49 barrier P & L upside error downside error
Extremal relative P & L
-60000% -50000% -40000% -30000% -20000% -10000% 0% 10000% 1.31 1.33 1.351.37 1.39 1.41 1.43 1.451.47 1.49 barrier rel. P & L in CHF
max rel upside error max rel downside err
5.2
Analysis of USD-JPY
We used the market and contract data listed in Table 6. Again the analysis looks very much like the EUR-USD case. We summarize the results in Table7
and Figure6.
Spot 110.00
Strike 100.00
Trading days 250 Domestic interest rate 0.03% (JPY) Foreign interest rate 2.17% (USD) Volatility 9.15% Time to maturity 1 year Notional 1,000,000 USD
Table 6: USD-JPY testing parameters
barrier 133.00 <10k <20k <30k <40k <50k <60k <70k upside error 949563 957 29 34 18 20 19 downside error 47623 1260 32 25 23 23 21 barrier 133.00 <80k <155k <175k more upside error 21 39 3 0 downside error 13 34 0 234
Table 7: USD-JPY distribution of absolute errors in JPY. The figures are the number of occurrences out of 1 million
hedging error with 99,9% confidence band -2000 -1800 -1600 -1400 -1200 -1000 -800 -600 -400 -200 0 111 113 115 117 119 121 123 125 127 129 131 133 135 barrier error in JPY hedge error confidence intervall Probability of mishedging 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00% 111 113 115 117 119 121 123 125 127 129 131 133 135 barrier probability
relative error with 99,9% confidence band
-120.00% -100.00% -80.00% -60.00% -40.00% -20.00% 0.00% 111 113 115 117 119 121 123 125 127 129 131 133 135 barrier error rel. error confidence band
relative error with 99,9% confidence band
-8% -7% -6% -5% -4% -3% -2% -1% 0% 113115 117119121 123125 127129 131133 135 barrier error rel. error confidence band
Extremal P & L for the short position
-30000000 -25000000 -20000000 -15000000 -10000000 -5000000 0 5000000 111 113 115 117 119 121 123 125 127 129 131 133 135 barrier P & L in JPY upside error downside error
Extremal relative error
-25000% -20000% -15000% -10000% -5000% 0% 5000% 113 115 117 119 121 123 125 127 129 131 133 135 barrier relative error
max positive rel error max negative rel error
5.3
Analysis of EUR-GBP
To compare we take now EUR-GBP as a currency pair without the USD. We used the market and contract data listed in Table8. Again, we observe the usual picture, i.e., a similar hedging error curvature as in EUR-USD. We summarize the results in Table9and Figure7.
Spot 0.6700
Strike 0.6700
Trading days 250 Domestic interest rate 5.17% (GBP) Foreign interest rate 2.27% (EUR) Volatility 7.65% Time to maturity 1 year Notional 1,000,000 EUR
Table 8: EUR-GBP testing parameters
barrier 0.7100 <1k <2k <4k0 <41k <42k upside error 950005 0 0 0 0 downside error 49711 3 59 220 2 barrier 0.7400 <1k <2k <7k0 <71k <72k upside error 978884 139 0 0 0 downside error 20493 273 48 162 1 barrier 0.7800 <1k <2k <3k <4k <5k upside error 994032 678 122 11 2 downside error 4001 860 183 27 2 barrier 0.7800 <109k <11k0 <111k <112k <114k upside error 0 0 0 0 0 downside error 1 15 63 2 1
Table 9: EUR-GBP distribution of absolute errors in GBP. The figures are the number of occurrences out of 1 million
Hedge error with 99,9% confidence band -25 -20 -15 -10 -5 0 5 0.680.7 0.720.740.760.780.8 0.820.840.860.880.9 0.92 barrier error in GBP hedge error confidence band probability of mishedging 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00% 20.00% 0.68 0.7 0.720.740.760.78 0.80.820.84 0.86 0.88 0.90.92 barrier probability probability
rel hedge error with 99,9% confidence band
-30.00% -25.00% -20.00% -15.00% -10.00% -5.00% 0.00% 5.00% 0.68 0.70.72 0.74 0.76 0.78 0.8 0.82 0.840.86 0.88 0.90.92 barrier error
rel hedge error confidence band
rel hedge error with 99,9% confidence band
-1.80% -1.60% -1.40% -1.20% -1.00% -0.80% -0.60% -0.40% -0.20% 0.00% 0.20% 0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92 barrier error
rel hedge error confidence band
Extremal P & L for the short position
-250000 -200000 -150000 -100000 -50000 0 50000 0.680.7 0.720.740.760.780.8 0.820.840.860.880.9 0.92 barrier P & L upside error downside error Relative P & L -2500% -2000% -1500% -1000% -500% 0% 500% 0.710.73 0.750.77 0.79 0.810.83 0.850.87 0.890.91 barrier P & L in GBP
max upside error max downside error
References
[1] Anagnou-Basioudis, I. andHodges, S. (2004)Derivatives Hedging and Volatility Errors. Warwick University Working Paper.
[2] Brown, B., Lovato, J. and Russell, K. (2004). CDFLIB - C++ - library, http://www.csit.fsu.edu/~burkardt/cpp_src/ dcdflib/dcdflib.html
[3] FusaiG. andRecchioni, C. (2003).Numerical Valuation of Discrete Bar-rier OptionsWarwick University Working Paper.
[4] H¨orfelt, P. (2003). Extension of the corrected barrier approximation by Broadie, Glasserman, and Kou.Finance and Stochastics,7, 231-243. [5] Matsumoto, M. (2004). Homepage of Makoto Matsumoto on the server
of the university of Hiroshima: http://www.math.sci.hiroshima-u.ac. jp/~m-mat/eindex.html
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Early Warning Systems of Financial Crises - Implementation of a currency crisis model for Uganda 2004 58. Heimer, Thomas / Köhler, Thomas
Auswirkungen des Basel II Akkords auf österreichische KMU 2004
57. Heidorn, Thomas / Meyer, Bernd / Pietrowiak, Alexander
Performanceeffekte nach Directors´Dealings in Deutschland, Italien und den Niederlanden 2004 56. Gerdesmeier, Dieter / Roffia, Barbara
The Relevance of real-time data in estimating reaction functions for the euro area 2004 55. Barthel, Erich / Gierig, Rauno / Kühn, Ilmhart-Wolfram
Unterschiedliche Ansätze zur Messung des Humankapitals 2004
54. Anders, Dietmar / Binder, Andreas / Hesdahl, Ralf / Schalast, Christoph / Thöne, Thomas Aktuelle Rechtsfragen des Bank- und Kapitalmarktrechts I :
Non-Performing-Loans / Faule Kredite - Handel, Work-Out, Outsourcing und Securitisation 2004 53. Polleit, Thorsten
The Slowdown in German Bank Lending – Revisited 2004
52. Heidorn, Thomas / Siragusano, Tindaro
Die Anwendbarkeit der Behavioral Finance im Devisenmarkt 2004
51. Schütze, Daniel / Schalast, Christoph (Hrsg.)
Wider die Verschleuderung von Unternehmen durch Pfandversteigerung 2004
50. Gerhold, Mirko / Heidorn, Thomas
Investitionen und Emissionen von Convertible Bonds (Wandelanleihen) 2004
49. Chevalier, Pierre / Heidorn, Thomas / Krieger, Christian
Temperaturderivate zur strategischen Absicherung von Beschaffungs- und Absatzrisiken 2003 48. Becker, Gernot M. / Seeger, Norbert
Internationale Cash Flow-Rechnungen aus Eigner- und Gläubigersicht 2003
47. Boenkost, Wolfram / Schmidt, Wolfgang M.
Notes on convexity and quanto adjustments for interest rates and related options 2003 46. Hess, Dieter
Determinants of the relative price impact of unanticipated Information in U.S. macroeconomic releases
2003 45. Cremers, Heinz / Kluß, Norbert / König, Markus
Incentive Fees. Erfolgsabhängige Vergütungsmodelle deutscher Publikumsfonds 2003
44. Heidorn, Thomas / König, Lars
Investitionen in Collateralized Debt Obligations 2003
43. Kahlert, Holger / Seeger, Norbert
41. Overbeck, Ludger / Schmidt, Wolfgang
Modeling Default Dependence with Threshold Models 2003
40. Balthasar, Daniel / Cremers, Heinz / Schmidt, Michael
Portfoliooptimierung mit Hedge Fonds unter besonderer Berücksichtigung der Risikokomponente 2002 39. Heidorn, Thomas / Kantwill, Jens
Eine empirische Analyse der Spreadunterschiede von Festsatzanleihen zu Floatern im Euroraum
und deren Zusammenhang zum Preis eines Credit Default Swaps 2002
38. Böttcher, Henner / Seeger, Norbert
Bilanzierung von Finanzderivaten nach HGB, EstG, IAS und US-GAAP 2003
37. Moormann, Jürgen
Terminologie und Glossar der Bankinformatik 2002
36. Heidorn, Thomas
Bewertung von Kreditprodukten und Credit Default Swaps 2001
35. Heidorn, Thomas / Weier, Sven
Einführung in die fundamentale Aktienanalyse 2001
34. Seeger, Norbert
International Accounting Standards (IAS) 2001
33. Stehling, Frank / Moormann, Jürgen
Strategic Positioning of E-Commerce Business Models in the Portfolio of Corporate Banking 2001 32. Strohhecker, Jürgen / Sokolovsky, Zbynek
Fit für den Euro, Simulationsbasierte Euro-Maßnahmenplanung für Dresdner-Bank-Geschäftsstellen 2001 31. Roßbach, Peter
Behavioral Finance - Eine Alternative zur vorherrschenden Kapitalmarkttheorie? 2001 30. Heidorn, Thomas / Jaster, Oliver / Willeitner, Ulrich
Event Risk Covenants 2001
29. Biswas, Rita / Löchel, Horst
Recent Trends in U.S. and German Banking: Convergence or Divergence? 2001
28. Löchel, Horst / Eberle, Günter Georg
Die Auswirkungen des Übergangs zum Kapitaldeckungsverfahren in der Rentenversicherung auf die Kapitalmärkte 2001 27. Heidorn, Thomas / Klein, Hans-Dieter / Siebrecht, Frank
Economic Value Added zur Prognose der Performance europäischer Aktien 2000
26. Cremers, Heinz
Konvergenz der binomialen Optionspreismodelle gegen das Modell von Black/Scholes/Merton 2000 25. Löchel, Horst
Die ökonomischen Dimensionen der ‚New Economy‘ 2000
24. Moormann, Jürgen / Frank, Axel
Grenzen des Outsourcing: Eine Exploration am Beispiel von Direktbanken 2000
23. Heidorn, Thomas / Schmidt, Peter / Seiler, Stefan
Neue Möglichkeiten durch die Namensaktie 2000
22. Böger, Andreas / Heidorn, Thomas / Graf Waldstein, Philipp
Hybrides Kernkapital für Kreditinstitute 2000
21. Heidorn, Thomas
Entscheidungsorientierte Mindestmargenkalkulation 2000
20. Wolf, Birgit
Die Eigenmittelkonzeption des § 10 KWG 2000
19. Thiele, Dirk / Cremers, Heinz / Robé, Sophie
Beta als Risikomaß - Eine Untersuchung am europäischen Aktienmarkt 2000
18. Cremers, Heinz
Optionspreisbestimmung 1999
17. Cremers, Heinz
Value at Risk-Konzepte für Marktrisiken 1999
16. Chevalier, Pierre / Heidorn, Thomas / Rütze, Merle
Gründung einer deutschen Strombörse für Elektrizitätsderivate 1999
15. Deister, Daniel / Ehrlicher, Sven / Heidorn, Thomas
CatBonds 1999
14. Jochum, Eduard
12. Heidorn, Thomas
Kreditrisiko (CreditMetrics) 1999
11. Moormann, Jürgen
Terminologie und Glossar der Bankinformatik 1999
10. Löchel, Horst
The EMU and the Theory of Optimum Currency Areas 1998
09. Löchel, Horst
Die Geldpolitik im Währungsraum des Euro 1998
08. Heidorn, Thomas / Hund, Jürgen
Die Umstellung auf die Stückaktie für deutsche Aktiengesellschaften 1998
07. Moormann, Jürgen
Stand und Perspektiven der Informationsverarbeitung in Banken 1998
06. Heidorn, Thomas / Schmidt, Wolfgang
LIBOR in Arrears 1998
05. Jahresbericht 1997 1998
04. Ecker, Thomas / Moormann, Jürgen
Die Bank als Betreiberin einer elektronischen Shopping-Mall 1997
03. Jahresbericht 1996 1997
02. Cremers, Heinz / Schwarz, Willi
Interpolation of Discount Factors 1996
01. Moormann, Jürgen
Lean Reporting und Führungsinformationssysteme bei deutschen Finanzdienstleistern 1995
HFB– SONDERARBEITSBERICHTE DER HFB- BUSINESS SCHOOL OF FINANCE & MANAGEMENT
No. Author/Title Year
01. Nicole Kahmer / Jürgen Moormann
Studie zur Ausrichtung von Banken an Kundenprozessen am Beispiel des Internet
(Preis: € 120,--) 2003
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