1. Consider a European call option when the stock price is $30, the exercise pri
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Question
1. Consider a European call option when the stock price is $30, the exercise price is $25, the time to maturity is 6 months, the volatility is 35% per annum, and the risk-free rate is 5% per annum. The stock is expected to pay $1 dividend in 2 months and another $1 dividend in 5 months. Use the Black-Scholes formula to price the call option.
2. Consider a stock index currently standing at 2,100. The dividend yield on the index is 3% per annum and the risk-free rate is 1%. A 3-month European call option on the index with a strike price of 2,000 is trading at $105.91. What is the value of a 3-month European put option with a strike price of 2,000? (Hint: Use put-call parity for index options)
Explanation / Answer
1. call value=5.3651 for 2 months
call value=6.1123 for 5 months
S0 = underlying price (USD per share)
X = strike price (USD per share)
= volatility (% p.a.)
r = continuously compounded risk-free interest rate (% p.a.)
q = continuously compounded dividend yield (% p.a.)
t = time to expiration (% of year)
call option=S0*e-qt *n(d1)- Xe-rt*n(d2)
d1=ln(so/x)+t(r-q+2/2)/root t
d2=d1- root t
2. C-P=S-D*K
Call - Put = (Stock + Interest - Dividends) - PV(Strike)
Or, simplified;
Call - Put = FV(Stock) - PV(Strike)
Where FV = Future Value and PV = Present Value.
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