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Formula Sheet: C S N d Xe N d S X r+ σ τ σ τ

This document provides formulas for calculating values related to European call and put options on non-dividend stocks. It shows the pricing formulas for calls and puts, as well as formulas for delta, theta, rho, vega, and gamma for both calls and puts. Key variables in the formulas include the stock price, strike price, risk-free interest rate, time to expiration, and stock volatility.

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Muneeb Aman
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46 views2 pages

Formula Sheet: C S N d Xe N d S X r+ σ τ σ τ

This document provides formulas for calculating values related to European call and put options on non-dividend stocks. It shows the pricing formulas for calls and puts, as well as formulas for delta, theta, rho, vega, and gamma for both calls and puts. Key variables in the formulas include the stock price, strike price, risk-free interest rate, time to expiration, and stock volatility.

Uploaded by

Muneeb Aman
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Formula Sheet

Call options
For a European option on a non-dividend stock call option can be written as:
−rτ
Ct =S t N ( d 1 )− Xe N ( d2)

St σ 2s

d 1=
ln ( )(
X
+ r+
2
τ )
σ s√τ

S    
2
ln  t    r  s  
X  2 
d2   d1  s 
s 

For a European call option on a non-dividend stock, delta can be shown as

  N(d1 )

For a European call option on a non-dividend stock, theta can be written as:

St  s
  N(d1 )  rX  e  r N(d 2 )
2 
For a European call option on a non-dividend stock, rho can be shown as

rho  X  e  r N(d 2 )

For a European call option on a non-dividend stock, vega can be shown as

  St   N  d1 

For a European call option on a non-dividend stock, gamma can be shown as

1
 N  d1 
St  s 
d12
∂ N ( d 1) 1 −
2
N ' ( d 1)= = e
∂ d1 √2π
For a European call option on a non-dividend stock, the sensitivity can be shown as

C t
 e  r N(d 2 )
X
Put Options
The price of put option on a non-dividend stock can be written as:

Pt  Xe r N  d 2   St N  d1 

St σ2

d 1=
ln ( )(
X
+ r+ s τ
2 )
σ s√τ

 St    s 
2
ln     r   
X  2 
d2   d1  s 
s 

τ =T −t
For a European put option on a non-dividend stock, delta can be shown as

  N(d1 )  1

For a European put option on a non-dividend stock, theta can be shown as

St s
  N(d1 )  rX  e  r N(d 2 )
2 

For a European put option on a non-dividend stock, vega can be shown as

  St   N  d1 

For a European put option on a non-dividend stock, rho can be shown as

rho   X  e  r N(d 2 )

For a European put option on a non-dividend stock, gamma can be shown as

1
 N  d1 
St  s 

For a European put option on a non-dividend stock, the sensitivity can be shown as

Pt
 e  r N( d 2 )
X

Whereas

N(-d2) =1-N(d2)

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