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

Price a European call option on non-dividend paying stock by
using a binomial tree. Stock price is €50, volatility is 26%
(p.a.), the risk-free interest rate is 5% (p.a. continuously
compounded), strike is € 55, and time to expiry is 6 months. How
large is the difference between the Black-Scholes price and the
price given by the binomial tree?

Price a European call option on non-dividend paying stock by
using a binomial tree. Stock price is €50, volatility is 26%
(p.a.), the risk-free interest rate is 5% (p.a. continuously
compounded), strike is € 55, and time to expiry is 6 months. How
large is the difference between the Black-Scholes price and the
price given by the binomial tree?

Question 3. Consider a six-month European call option on a stock
index. The current value of the index is 1,200, the strike price is
1,250, the risk-free rate is 5%. The index volatility is 20%.
Calculate: a) the value of the option
b) the delta of the option
c) the gamma of the option
d) the theta of the option
e) the vega of the option
f) the rho of the option
assume q = 0.

Calculate the implied volatility using the following
information:
stock price 80.00
call option price 11.38
option time to expiration 2 months
option strike price 70.00
risk free rate 4%
the choices are A. 25% B.30% C.35% D.20% how to arrive at the
answer using regular excel

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