Question

A bank has sold for $250,000 a European call option on 100,000 shares of a non-dividend paying stock. Current stock price is $40, Strike is $50, risk-free rate is 5%, volatility is 25%, and the consider 10 weeks. Construct a delta-neutral hedge for this bank and compute the profit/loss at the end of the 10-week period.

Answer 1

Per share price $250000/100000= $2.5 per share

Delta Hedging•This involves maintaining a delta neutral portfolio•The delta of a European call on a non-dividend-paying stock isN (d1)•The delta of a European put on the stock is [N(d1) – 1]

Delta Hedgingcontinued•The hedge position must be frequently rebalanced•Delta hedging a written option involves a “buy high, sell low” trading rule

Hence

S=40, K=50, R=5%, ¶=25%

T= 10 weeks

Profit/loss of 10 weeks period is $4.88 loss.