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Markov chains and the pricing of derivatives

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Figure 2.1: The layout of the two dimensional grid for X 1,n and X 2,n . The intensities λ u 1,n , λ u 2,n , λ d 1,n , λ d 2,n are denoted as up 1 , up 2 , down 1 , down 2 respectively
Table 2.1: The prices of European spread options with the payoff, max(S T 1 − S T 2 , 0), on two lognormal assets with maturity T = 0.5 years
Table 3.1: Conditions on the discriminant and the real roots α(x), α(x), assumed to satisfy the relation α(x) ≤ α(x), in this table refer to the parabolas that arise in inequalities (3.40), (3.41) and (3.42)
Table 3.2: Implied volatility in the CEV model. The maturity T varies from half a year to two years and the corresponding strikes are of the form Ke rT , where K takes values between 80 and 120 and the risk-free rate equals r = 2%
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Outline

Non-uniform grid generation algorithm and numerical results Approximation of the realized variance dynamics Markov chain approximation Volatility derivatives – the continuous case Volatility derivatives – the discontinuous case Forward starting options and the volatility index Pricing and hedging of vanilla options and forward-starts Calibration to the vanilla surface

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