Faculty of Economics and Business
Department of Business
FINANCE I (102329) – Group 3 – 2012-13
Study Guide. Dr. Maria-Antonia Tarrazon & Dr. Joan Montllor
1
EXERCISE 9: WILD STRAWBERRIES, Ltd
Solved example on (1) Option pricing through one-step binomial trees and risk-neutral
probabilities and (2) Arbitrages with unfairly valued options
A stock of the company Wild Strawberries Ltd is currently worth 100€. In one year the stock price
may become 125€, if demand for the products of this firm is high, or 80€, if its newest product fails
to persuade customers of its magnificent performance.
European call and put options on one stock of Wild Strawberries Ltd are traded on the derivatives
market with a strike price of 95€ and maturity in one year. Current prices for these two options are
10€ (call) and 12.50€ (put).
The risk-free interest rate is 2.5% per annum.
Questions:
1. Calculate the call value and the put value a) according to the one-step binomial method and b)
following a risk-neutral valuation.
2. Write the put-call parity for this case. Why is it possible to establish this relationship?
3. Are there arbitrage opportunities with these options? If so, develop them.
SOLUTION
1. Evolution of the underlying asset (= one stock of Wild Strawberries Ltd):
125
100
80
Evolution of the call option:
Max [0, 125-95]= 30
c0 (?)
Max [0, 80–95] = 0
Calculation of the call value (fair/right price or price in equilibrium):
a) Using the one-step binomial method and synthetic portfolio approach
125· + B·1.025 = 30 = 2/3 shares (>0 long position or purchase of 2/3 of one share)
80· + B·1.025 = 0 B = -52.03 € (< 0 short position or borrowing of 52.03 € at rf=2.5%)
Call price: c0 = 100·(2/3) – 52.03 = 14.64 €
