Question

Let S = $100, K = $120, σ = 30%, r = 0.08, and δ = 0. Compute the Black-Scholes call price for 2 year to maturity with dividend yield of 0.001.

Answer #1

As per Black Scholes Model | ||||||

Value of call option = S*N(d1)-N(d2)*K*e^(-r*t) | ||||||

Where | ||||||

S = Current price = | 100 | |||||

t = time to expiry = | 2 | |||||

K = Strike price = | 120 | |||||

r = Risk free rate = | 8.0% | |||||

q = Dividend Yield = | 0.1% | |||||

σ = Std dev = | 30% | |||||

d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2) | ||||||

d1 = (ln(100/120)+(0.08-0.001+0.3^2/2)*2)/(0.3*2^(1/2)) | ||||||

d1 = 0.154806 | ||||||

d2 = d1-σ*t^(1/2) | ||||||

d2 =0.154806-0.3*2^(1/2) | ||||||

d2 = -0.269458 | ||||||

N(d1) = Cumulative standard normal dist. of d1 | ||||||

N(d1) =0.561513 | ||||||

N(d1) = Cumulative standard normal dist. of d2 | ||||||

N(d2) =0.393789 | ||||||

Value of call= 100*0.561513-0.393789*120*e^(-0.08*2) | ||||||

Value of call= 15.88 |

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A stock’s current price S is $100. Its return has a volatility
of s = 25 percent per year. European call and put options trading
on the stock have a strike price of K = $105 and mature after T =
0.5 years. The continuously compounded risk-free interest rate r is
5 percent per year. The Black-Scholes-Merton model gives the price
of the European put as:
please provide explanation

In addition to the five factors, dividends also affect the price
of an option. The Black–Scholes Option Pricing Model with dividends
is:
C=S×e−dt×N(d1)−E×e−Rt×N(d2)C=S×e−dt×N(d1)−E×e−Rt×N(d2)
d1=[ln(S/E)+(R−d+σ2/2)×t](σ−t√)d1= [ln(S /E ) +(R−d+σ2/2)×t ] (σ−t)
d2=d1−σ×t√d2=d1−σ×t
All of the variables are the same as the Black–Scholes model
without dividends except for the variable d, which is the
continuously compounded dividend yield on the stock.
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A stock is currently traded for $135. The risk-free rate
is 0.5% per year (continuously compounded APR) and the stock’s
returns have an annual standard deviation (volatility) of 56%.
Using the Black-Scholes model, we can find prices for a call and a
put, both expiring 60 days from today and having strike prices
equal to $140.
(a) What values should you use for S, K, T−t, r, and σ
in the Black-Scholes formula?
S =
K =
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