Errata for Section 38 of the Actuary's Free Study Guide for Exam 3F / Exam MFE

Note: This is a correction for the solution to Problem ESQBSF5 from Section 38 of The Actuary's Free Study Guide for Exam 3F / Exam MFE. In the original solution, ln(K/S) was mistakenly used instead of ln(S/K). My apologies for the inconvenience.

Problem ESQBSF5.

Similar to Question 6 from the Society of Actuaries' Sample MFE Questions and Solutions:

Athena wishes to purchase 204 European call options on the stock of Mythology Co. The stock currently trades for $40 per share, and pays dividends at an annual continuously-compounded yield of 0.11. The annual continuously-compounded risk-free interest rate is 0.09, and the relevant measure of volatility is 0.1.

The strike price of the options is $43, and the options will expire in 5 years. Use the Black-Scholes formula to find the price of the block of 204 call options.

Solution ESQBSF5.

First, we find d₁ = [ln(40/43) + (0.09 - 0.11 + 0.5*0.1²)5]/[0.1√(5)] = d₁ = -0.6588380276

Now we find d₂ = d₁ - σ√(T) = -0.0119823657 - 0.1√(5) = d₂ = -0.8824448253

In MS Excel, using the input "=NormSDist(-0.6588380276)", we find that N(d₁) = 0.254999892

In MS Excel, using the input "=NormSDist(-0.8824448253)", we find that N(d₂) = 0.188768152

Now we use the Black-Scholes formula:

C(S, K, σ, r, T, ∂) = Se^-∂TN(d₁) - Ke^-rTN(d₂) = 40e^-0.11*50.254999892 - 43e^-0.09*50.188768152 =

C(S, K, σ, r, T, ∂) = 0.7092383961

We want to find 204C = 204*0.7092383961 = $144.6846328

See other sections of The Actuary's Free Study Guide for Exam 3F / Exam MFE.