Q.78 A Treasury department analyst calculates that the open EUR currency position of Garden Bank is EUR 1,000,000. The Euro is currently worth USD 1.15, and the exchange rate has an annual volatility of 25%. The risk-free rates on USD and EUR are 2% and 0.5%, respectively. To hedge the position, the analyst suggests selling a 3-month call option with a strike price of 1.1. What is the price of the European call option using a one-step binomial tree model? | Financial Risk Manager Part 1 Quiz - LeetQuiz
Financial Risk Manager Part 1
Explanation:
The parameters given for the pricing are:
S0=1.15K=1.1T=123=0.25σ=0.25r=0.02 (domestic risk-free rate, USD)
rf=0.005 (foreign risk-free rate, EUR)
First, we calculate the up (u) and down (d) factors for the one-step binomial model:
u=eσT=e0.25×0.25=e0.125≈1.13315d=e−σT=e−0.125≈0.88250
Next, find the option's payoffs at the up and down nodes:
Su=S0×u=1.15×1.13315=1.30312Cu=max(Su−K,0)=max(1.30312−1.1,0)=0.20312Sd=S0×d=1.15×0.88250=1.01487Cd=max(Sd−K,0)=0
Now compute the risk-neutral probability of an up move (p):
a=e(r−rf)T=e(0.02−0.005)×0.25=e0.00375≈1.00376p=u−da−d=1.13315−0.882501.00376−0.88250=0.250650.12126≈0.48378
Finally, calculate the current price of the call option by discounting the expected payoff:
C=e−rT[p×Cu+(1−p)×Cd]C=e−0.02×0.25[0.48378×0.20312+(1−0.48378)×0]C=e−0.005×0.098265≈0.99501×0.098265≈0.097775 USD
Rounding to 4 decimal places gives USD 0.0978.
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Q.78 A Treasury department analyst calculates that the open EUR currency position of Garden Bank is EUR 1,000,000. The Euro is currently worth USD 1.15, and the exchange rate has an annual volatility of 25%. The risk-free rates on USD and EUR are 2% and 0.5%, respectively. To hedge the position, the analyst suggests selling a 3-month call option with a strike price of 1.1. What is the price of the European call option using a one-step binomial tree model?