Question

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 = $50, u = 1.3 and d = 0.8 . The calls will mature in two time steps and have strike price K = $50 . Over each time step the return is a constant R = 1.01 . (a) Calculate the premium of one call. (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. (d) If the 100 calls are exercised at maturity, then the writer must be able to sell 100 shares to the holder. Show how the writer obtains these 100 shares, while also settling any debt in the hedge portfolio, without making a profit or a loss.

Answer 1