In this problem, we consider an asset-or-nothing call option that gives its owner a share of the underlying stock if the

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In This Problem We Consider An Asset Or Nothing Call Option That Gives Its Owner A Share Of The Underlying Stock If The 1 (134.77 KiB) Viewed 24 times

In this problem, we consider an asset-or-nothing call option that gives its owner a share of the underlying stock if the stock price exceeds a certain level K and zero otherwise. In the Black-Scholes model, the price of this call option is computed using: C = e-E2(S(T)1s(T)>K, where 1s(T)>k is the indicator function that takes the value of 1 when S(T) > K and zero otherwise. Assume a non-dividend-paying stock which has the following dynamics in the risk-neutral world: ds rSdt +oSDW. = = a) Derive the analytical solution to the price of an asset-or-nothing call option and show that the price is given by log (%) +(+0.502)T C = SN(di), where di OVT Note that you should show all steps in your derivation. b) Derive the formula for the option's sensitivity to the to changes in the risk- free rate of interest. Specifically, derive the expression for Based on your result, discuss how the interest rate affects the price of an asset-or- nothing call option. ac dr.