Question

1:Consider a European call option on a stock with current price $100 and volatility 25%. The stock pays a $1 dividend in 1 month. Assume that the strike price is $100 and the time to expiration is 3 months. The risk free rate is 5%. Calculate the price of the the call option.

2: Consider a European call option with strike price 100, time to expiration of 3 months. Assume the risk free rate is 5% compounded continuously. If the underlying is at price $100 and has volatility of 30%, what is the delta of the option? (Calculate your answer to the nearest hundredth.)

3: Consider a European call option with strike price 100, underlying price of 98, time to expiration of 3 months, and risk free rate of 5% (compounded continuously). The stock does not pay a dividend. If the call premium is $5.51, what is the implied volatility? (Hint: Use excel to calculate the Black-Scholes formula and then adjust the volatility to find the implied volatility.)

4: Consider an option with theta = -14.3. If a week passes by, and the underlying stock price doesn't change, nor does any of the other parameters (interest rate, volatility, etc.) by how much to you expect the price of the option to have changed. (Make sure to get the sign correct. An increase in the price should be positive and a decrease should be negative.) Use 1/52 to represent a week in years.

5:  The vega of an option is 19.7. If the volatility increases from 30% to 32%, by how much do you expect the option price to change (assume all other parameters do not change).  

Answer 1

answer 1:

Call price ie C0 = S0 N(d1) - E/rt * N(d2)

where,

d1= ln(S0/E) +[r + 2/2]*t /*root t

d2= d1 - *root t

S0 =100-1/e.05*.08

= 100-1/1.0040

=99.004

ln(S0/E) = ln 99.004

= -.01005

d1= -.01005+[.05+.25*.25/2]*.25/0.25*0.25

=0.0821

N(d1) = 0.49204(after solving eqn)

N(d2)=0.4801

C0=100*0.49204-100/e0.05*0.25*0.4801

=49.204-47.4135

= 1.79 approx