Classification of Calls and Puts: Practice Problems and Solutions

The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 7

This section of sample problems and solutions is a part of The Actuary's Free Study Guide for Exam 3F / Exam MFE, authored by Mr. Stolyarov.

This is Section 7 of the Study Guide. See Section 1 here. See Section 2 here. See Section 3 here. See Section 4 here

. See Section 5 here. See Section 6 here.

This is the generalized formula for currency options - relating calls denominated in one currency (say, the dollar or any other currency A of our choice) to puts denominated in another currency (say, the euro or any other currency B of our choice). We will use this formula in our exploration of how puts and calls are classified with relation to our choice of the underlying asset and the strike asset.

C_A(x₀, K, T) = x₀ K P_B(1/x₀, 1/K, T)

Explanation of variables:

K = strike price, denominated in currency A.

T = time to expiration of the options.

x₀ = exchange rate in terms of [currency A/currency B].

C_A(x₀, K, T) = price of A-denominated call option on B (in units of currency A).

P_B(1/x₀, 1/K, T) = price of B-denominated put option on A (in units of currency B).

Source: McDonald, R.L., Derivatives Markets (Second Edition), Addison Wesley, 2006, Ch. 9, p. 292.

Problem CCP1. Bard Co. stock and Drab Co. stock are used as underlying or strike assets in writing options contracts. Geoffrey owns an option contract with the following payoff: max(0, S_Bard - S_Drab). Which of the following are correct ways of describing this contract? More than one answer may be correct.

(a) A call option on Bard stock with Drab stock as the strike asset.

(b) A call option on Drab stock with Bard stock as the strike asset.

(c) A put option on Bard stock with Drab stock as the strike asset.

(d) A put option on Drab stock with Bard stock as the strike asset.

(e) A call option on both Bard and Drab stock.

(f) A put option on both Bard and Drab stock.

Solution CCP1.

For Geoffrey, if Bard is the underlying asset, then Geoffrey can gain at expiration if the price of Bard exceeds the price of Drab - so this option functions as a Bard call.