# What would be the issue price of the following contract?

• Stock currently A has a price equal to 100.
• Stock B also currently has a price of 100.
• The contract has a maturity $\mu$ of one year.
• At maturity the payout is the max price of either A or B.

What is the contract worth at issue?

## 2 Answers

The actual answer depends on the volatility of both assets and their correlation, assuming for simplicity that rates and dividends are zero.

With what you’re given you should be able to at least answer that it’s worth more than 100 (rates are 0), and to show this you can simply express max(A,B) as B + Max(A-B,0). Take the expected value in the risk-neutral world to price it. The second term is a so-called exchange option obviously whose value is > 0. This is straightforwardly valued in a BS framework (see Margrabe formula). The first term is 100 if rates and dividends are zero.

This is probably a homework question... that being said this should be valued similar to how you value an option. Except the payout would be: max(A,B) instead of max(St-k,0) for a call. Because it doesn’t give any volatility parameters there’s not a whole lot you can say other than assume the contract is worth 100 discounted for a year at the risk free rate.

• This is coming from the interview question space. Discounting would have been my first instinct as well, but apparently this is wrong. Perhaps one is meant to inquire about the volatilities. – A.L. Verminburger Feb 25 '18 at 16:34
• How? That doesn’t make any sense... All options and futures are discounted at the risk free rate. If there’s no discounting then you can arbitrage with it. – Dayton Marks Feb 26 '18 at 0:21