Question
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
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
= 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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