Question

URGENT !

Consider a call option on a stock, the stock price is $29, the strike price is $30, the continuously risk-free interest rate is 5% per annum, the volatility is 20% per annum and the time to maturity is 0.25.

(i) What is the price of the option? (6 points)

(ii) What is the price of the option if it is a put? (6 points)

(iii) What is the price of the call option if a dividend of $2 is expected in 60 days? (8 points)

Answer 1

Black Scholes Options Formula

​

Where St is current market price of the underlying Asset

C is the Price of call option

N is the Normal Distribution table

K is the Strike Price of option

r is the risk free rate of interest

t is time period of Maturity

σv2 is the Volatility of Stock

Adjusted Stock Price (ASt) when dividend is in between the option value calculation date and expiration date

Where ASt is the adjusted Stock price

St is the stock price

D is the expected Dividend

R is the Annualised risk free Rate of Interest

t is the Annualised time of expected dividend (Dividend Date/365)

Given Information
Current Stock Price (St)	29	<<C2
Option Strike Price (K)	30	<<C3
Time of Maturity (Annualised) (t)	0.25	<<C4
Risk Free Interest Rate (Annualised) (r)	5%	<<C5
Annual Volatility of Stock - σ	20%	<<C6
Given Expected Dividend (D)	2.00	<<C7
Expected time of Dividend (days)	60	<<C8
Required Calculations
log(St/K)	-0.0339	=LN(C2/C3)
σ√t	0.1000	=SQRT(C4)*C6
σ2	0.0400	=C6^2
(r+σ2/2)t	0.0175	=(C5+(C13/2))*C4
d1	-0.1640	=(C11+C14)/C12
-d1	0.1640	=-C15
d2	-0.2640	=C15-C12
-d2	0.2640	=-C17
N(d1)	0.434859464	=NORM.S.DIST(C15,TRUE)
N(-d1)	0.565140536	=NORM.S.DIST(C16,TRUE)
N(d2)	0.395883981	=NORM.S.DIST(C17,TRUE)
N(-d2)	0.604116019	=NORM.S.DIST(C18,TRUE)
e-rt	0.9875778	=1/EXP(C5*C4)
Option Values
Call Option Value	0.8819	=(C2*C19)-(C3*C23*C21)
Put Option Value	1.5093	=(C3*C23*C22)-(C2*C20)
Call Option Values with Dividend Adjustment
Adsjusted Stock Price (ASt)	28.00818549	=C2-(1/EXP(C5*C8/365))
Adjusted log(St/K)	-0.068700575	=LN(C30/C3)
Adjusted d1	-0.512005752	=(C31+C14)/C12
Adjusted d2	-0.6120	=C32-C12
Adjusted N(d1)	0.304323492	=NORM.S.DIST(C32,TRUE)
Adjusted N(d2)	0.270266976	=NORM.S.DIST(C33,TRUE)
Call Option Values with Dividend Adjustment	0.5163	=(C30*C34)-(C3*C23*C35)

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