Question: In Financial Derivatives Consider the two-period, Binomial Options Pricing Model. The current stock price S= $105 and the risk-free rate r = 3% per period

In Financial Derivatives

Consider the two-period, Binomial Options Pricing Model. The current stock price S= $105 and the risk-free rate r = 3% per period (simple rate). Each period, the stock price can go either up by 10 percent or down by 10 percent. A European call option (on a non-dividend paying stock) with expiration at the end of two periods (n=2), has a strike price K = $100. The risk-neutral probability of an up move is q = (R-D)/(U-D), where R= 1+r.

a). Set out the stock price tree (e.g. in a table), calculate the (no-arbitrage) fair price of the call and explain the meaning of risk neutral valuation (RNV).

b). Calculate the hedge ratio at t=0 and explain how you can hedge 100 written calls at t=0. Calculate the value of the hedge portfolio at nodes U and D and hence show that the hedge-portfolio earns the risk-free rate over the first period (i.e. along the path from node t=0, either to node-D or node-U).

c). Calculate the hedge ratio at node-U and explain what this implies for delta hedging (over the next period).

(15 marks)

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