Answer to Question #156756 in Financial Math for Alv

Question

The Moon company currently sells for 100 $. The annual stock price volatility is %10 and risk- free interest rate %8, the price of a call on a company’s stock with strike price 200 $ and time period 2 months. Find the stock option price with Black and Scholes Model. If option market value 320 $ what is the option strategy?

Answer 1

$c=S0\times N(d1)-K\times N(d2)\times DF$$d1=\frac{ln(\frac{S0}{K})+(r+\frac{\sigma^2}{2})\times t}{ \sigma\times t^{0.5}}$

$d2=d1-\sigma\times t^{0.5}$

$DF=e^{-r\times t}$

S0=100

K=200

$\sigma=0.1$

r=0.08, 0.0067 years

t=2, 0.167 years

$DF=e^{-0.0067\times0.167}=0.999$

$d1=\frac{ln(\frac{100}{200})+(0.0067+\frac{0.1^2}{2})\times 0.167}{ 0.1\times0.167^{0.5}}=-0.6455$

$d2=-0.6455-0.1\times 0.167^{0.5}=0.6863$

$c=100\times N(-0.6455)-200\times N(-0.6863)\times0.999=-23.27$

K=320

$DF=e^{-0.0067\times0.167}=0.999$

$d1=\frac{ln(\frac{100}{320})+(0.0067+\frac{0.1^2}{2})\times 0.167}{ 0.1\times0.167^{0.5}}=-1.1155$

$d2=-1.1155-0.1\times 0.167^{0.5}=-1.1563$

$c=100\times N(-1.1155)-320\times N(-1.1563)\times0.999=-26.33$