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In this question numerical solutions must be accurate to six significant figures. A writer is currently selling 100 identical European calls and wants to minimise potential losses with self-financing dynamic hedging. In the Cox-Ross-Rubenstein notation, the underlying asset of these calls has S = $60, u=1.4 and d = 0.6. The calls will mature in two time steps and have strike price K = $60. Over each time step the return is a constant R = 1.06. Define t = 0 as the time the calls are sold, t = 1 as the end of the first time-step, and t = 2 as the end of the second time-step when the calls reach maturity.
(a) Calculate the premium of one call, given that the risk neutral probability is π = 0.575.
(b) Explain the hedging process at time t = 0 when the writer sells 100 calls. What investments must the writer have in the hedge portfolio and what are their values?
(c) Explain how the hedge portfolio changes over the first time-step and what the writer has to do at time t = 1 to maintain the self-financing dynamic hedging.
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