1) What is the value of a put option if the underlying stock price is $38, the s

Question

1)

What is the value of a put option if the underlying stock price is $38, the strike price is $31, the underlying stock volatility is 43 percent, and the risk-free rate is 4.4 percent? Assume the option has 149 days to expiration. (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

2)

A stock with a current price $57 has a put option available with a strike price of $54. The stock will move up by a factor of 1.26 or down by a factor of 0.89 over the next period and the risk-free rate is 3 percent. What is the price of the put option? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

3)

A stock is currently priced at $58 and has an annual standard deviation of 38 percent. The dividend yield of the stock is 2.2 percent, and the risk-free rate is 4.2 percent. What is the value of a call option on the stock with a strike price of $55 and 58 days to expiration? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Explanation / Answer

Formulas to be used.

Call Price, C(S,t)= N(d1)S- N(d2)Ke-r(T-t)

Put Price, P(S,t)= N(-d2) Ke-r(T-t) - N(-d1)S

d1= (1/(sd*(T-t)1/2)* (ln(S/K)+(r+sd2/2)(T-t)

d2= d1- sd*(T-t)1/2                                                               

where S- Spot Price; N(.)- Cummulative distribution function of the standard normal distribution; K- Strike Price;

(T-t)- Time to maturity; r- Risk Free Rate; sd- Volatility of returns of underlying asset

Part 1

S= $38; K=$31; sd= 43%= 0.43; r=4.4%= 0.044; T-t= 149 days= 149/365= 0.41 years

Using the above values in put price formula we can calculate its value.

d1= 0.94; d2= 0.66

Therefore N(d1)= 0.83; N(d2)= 0.75

Hence Put Option Price= $1.10968

Part 2

S= $57; K=$54; r=3%= 0.03; T-t= 149 days= 149/365= 0.41 years;

Sd= ((1.26*57-57)2+(0.89*57-57)2)^1/2(Formula for Volatility)= 16.09

Using the above values in put price formula we can calculate its value.

d1= 0.69; d2= 0.59

Therefore N(d1)= 0.76; N(d2)= 0.72

Hence Put Option Price= $0.89055

Part 3

S0= $58; K=$55; sd= 38%= 0.38; r=4.2%= 0.042; T-t= 58 days= 58/365= 0.16 years

Dividend Yield, q= 2.2%

When dividend yield is given the value to stock changes to S= S0*e(r-q)(T-t)

So S= 58.18

Using the above values in call price formula we can calculate its value.

d1= 0.49; d2= 0.33

Therefore N(d1)= 0.68; N(d2)= 0.63

Hence Call Option Price= $5.47935

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