Binomial Option Pricing with Puts: Practice Problems and Solutions

The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 19

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 19 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. See Section 7 here. See Section 8 here. See Section 9 here. See Section 10

here. See Section 11 here. See Section 12 here. See Section 13 here. See Section 14 here. See Section 15 here. See Section 16 here. See Section 17 here. See Section 18 here.

Binomial option pricing with puts can be done using the exact same formulas and conceptual tools developed in Sections 15-18 except that calculating the put price at expiration uses the formula P = max(0, K - S) instead of C = max(0, S - K).

Here, we will use one and two-period binomial models for all practice problems, because the objective of this section is to establish the conceptual approach to binomial option pricing with puts. Students should be aware that this approach can translate to larger multi-period models as well, using the same essential procedure as the one illustrated here.

Source: McDonald, R.L., Derivatives Markets (Second Edition), Addison Wesley, 2006, Ch. 10, pp. 328-329.

Original Practice Problems and Solutions from the Actuary's Free Study Guide:

Problem BOPWP1. The stock of Predictable Co. is currently worth $100 per share. In one year, this price can either be $120 or $90. Predictable Co. stock does not pay dividends. The annual continuously compounded risk-free interest rate is 5%. The strike price of a European put option on Predictable Co. stock is $130. Using, the one-period binomial option pricing model, find the price today of one such put option on Predictable Co. stock.

Solution BOPWP1. First, we consider the put option price tree

P - - - P_u

P - - - P_d

In one year, if the stock is worth $120, the put option will be worth P_u = 130 - 120 = 10.

If the stock is worth $90, the put option will be worth P_d = 130 - 90 = 40.

We are given ∂ = 0, r = 0.05, S = 100, h = 1, u = 1.2, and d = 0.9.

We can still use the same formula for the risk-neutral probability of the stock price's increase next year: