Question

A bank decides to create a five-year principal-protected note on a non-dividend-paying stock by offering investors a zero-coupon bond plus a bull spread created from calls. The risk-free rate is 4% and the stock price volatility is 25%. The low-strike-price option in the bull spread is at the money. What is the maximum ratio of the high strike price to the low strike price in the bull spread. Use DerivaGem.

help me with using DerivaGem please!

Answer 1

Assume that the amount invested is 100. (This is a scaling factor.) The amount available to create the option is 100-100e 0318127 The cost of the at the money option can be calculated from DerivaGem by setting the stock price equal to 100, the volatility equal to 25%, the risk-free interest rate equal to 4%, the time to exercise equal to 5 and the exercise price equal to 100. It is 30.313. We therefore require the option given up by the investor to be worth at least 30.313-18.127 - 12.186. Results obtained are as follows:

Strike	optional value
125	21.12
150	14.71
175	10.29
165	11.86

Continuing in this way we find that the strike must be set below 163.1. The ratio of the high strike to the low strike must therefore be less than 1.631 for the bank to make a profit.

(Excel's Solver can be used in conjunction with the DerivaGem functions to facilitate calculations.)