Consider the Black -Scholes model (SS)[0,71 and let 0 < To 0 is a fixed strike....

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Consider the Black -Scholes model (SS)[0,71 and let 0 < To 0 is a fixed strike. What is the limit for large N? (ii) Use the distribution from (i) and the Black -Scholes formula to compute the price of an geometric Asian call option with payoff n=1 Ave ds/so = rdt, ds/s = rdt + vdW19, 1/N Exercise 13 (Up-and-Out Call in the Heston Model, 7 points) Consider the risk-neutral Heston model (S0, S10.71, where the dynamics for an equidistant for N? of the safe and risky assets as well as the squared volatility process are modeled directly under a pricing measure Q. Suppose a liquidly traded European option is available as an additional hedging instrument (i) Derive a PDE for the price of an up-and-out call option. (ii) How can this barrier option be hedged by trading in the primary safe and risky assets, as well as the liquidly traded European option ? Exercise 10 (No-Arbitrage and Completeness 8 points) 5 Let S = 1,83 = 2 and let W, W2, W3 be three independent standard Brownian motions Explain which of the following discounted risky asset dynamics correspond to a market with an equivalent martingale measure . If no martingale measure exists, construct an arbitrage ! (1) dv = X(v - v)dt + 4 (pdW10 + - p dw ,9), 1,Q (2) (3) dS1/S2 dt+dW?, d$2/S2 = 1 dt + 2dW!, dS1/S1 = 2 dt+dW! - 2dW ds2/82-1dt- dw? + dw?. dS1/S2 dt+ sin (W3) dW1 - 2dW 2, ds2/82 1dtdw + dw2. Which of these markets are complete? Justify your argument! Consider the Black -Scholes model (SS)[0,71 and let 0 < To 0 is a fixed strike. What is the limit for large N? (ii) Use the distribution from (i) and the Black -Scholes formula to compute the price of an geometric Asian call option with payoff n=1 Ave ds/so = rdt, ds/s = rdt + vdW19, 1/N Exercise 13 (Up-and-Out Call in the Heston Model, 7 points) Consider the risk-neutral Heston model (S0, S10.71, where the dynamics for an equidistant for N? of the safe and risky assets as well as the squared volatility process are modeled directly under a pricing measure Q. Suppose a liquidly traded European option is available as an additional hedging instrument (i) Derive a PDE for the price of an up-and-out call option. (ii) How can this barrier option be hedged by trading in the primary safe and risky assets, as well as the liquidly traded European option ? Exercise 10 (No-Arbitrage and Completeness 8 points) 5 Let S = 1,83 = 2 and let W, W2, W3 be three independent standard Brownian motions Explain which of the following discounted risky asset dynamics correspond to a market with an equivalent martingale measure . If no martingale measure exists, construct an arbitrage ! (1) dv = X(v - v)dt + 4 (pdW10 + - p dw ,9), 1,Q (2) (3) dS1/S2 dt+dW?, d$2/S2 = 1 dt + 2dW!, dS1/S1 = 2 dt+dW! - 2dW ds2/82-1dt- dw? + dw?. dS1/S2 dt+ sin (W3) dW1 - 2dW 2, ds2/82 1dtdw + dw2. Which of these markets are complete? Justify your argument!

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Sure lets break down each exercise Exercise 12 Geometric Asian Option i To compute the distribution ... View the full answer