FINM3405L5 - Black Scholes Option Pricing Formula Lecture 5...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 5 ricing Options and Pricing Options and Hedging With Options lack Scholes Option Pricing Black Scholes Option Pricing Formula ± The BS formula values a European call option r i t tenona on ividend aying tocks written on a non-dividend -paying stocks () () 2 1 0 d N Xe d N S C rT E = ± S 0 is current stock price is e ercise/strike price ± X is exercise/strike price ± T is time to expiry (in years) i i kl t f i t t ± r is riskless rate of interest p.a. ± σ is the standard deviation of the stock return ( T T r X S d σ + + = 2 2 1 0 1 ) ( ) / ln( T d d = 1 2 N(d 1 ) and N(d 2 ) ± d 1 and d 2 are just preliminary calcs ± N( d 1 ) and N( d 2 ) are probability terms – their role is to assess the probability that the stock rice will exceed the strike price so that the price will exceed the strike price so that the option will end up being exercised at maturity (·) represents a standard normal cumulative ± N(·) represents a standard normal cumulative distribution function ok up probabilities in statistical tables – look up probabilities in statistical tables – use NORMSDIST(·) in Excel
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example: Black Scholes Price ± WPL share price (S 0 ) is $10.50 ± standard deviation ( σ ) is 30% pa ± riskless rate of return (r) is 5% ± call option with strike (X) of $10 and time to xpiry (T) of six months expiry (T) of six months () ( ) ln 2 2 1 0 + + = T r X S σ , 45 . 0 4539 . 0 5 . 0 3 . 0 05 . 0 00 . 10 50 . 10 ln 2 2 1 1 = + + = T d 5 . 0 3 . 0 = , 24 . 0 2379 . 0 5 . 0 3 . 0 45 . 0 1 2 = = T d d ( )( ) N N 2 1 0 = d Xe d S C rT E 948 753 0 736 0 0 24 . 0 N 10 45 . 0 N 50 . 10 5 . 0 05 . 0 = × e ( )( )( ) . 27 . 1 $ 5948 . 0 9753 . 0 10 6736 . 0 50 . 10 = × = 0 + = Xe S C P rT E E 52 . 0 $ 10 50 . 10 27 . 1 5 . 0 05 . 0 = + = × e Factors Influencing BS Price Increase in Effect on Call Value Effect on Put Value Stock price (S) Increase Decrease p( ) Strike price (X) Decrease Increase Time to expiry (T) Increase Increase Riskless rate (r) Increase Decrease Volatility ( σ ) Increase Increase
Background image of page 2
Effect of Share Price on Option Price ± Obviously, with a call option, you want share price rising (as far above strike as possible). So there is a positive relationship between S and call option price ± Conversely, with a put option, you want share price falling below strike (the lower the better). So there is a negative relationship between S and put option price. Effect of Strike Price on Option Price ± with a call option, you want share price rising bove strike So the lower the strike the above strike. So, the lower the strike, the better chance of finishing in-the-money egative lationship between nd call negative relationship between X and call option price ith a put option you want share price falling ± with a put option, you want share price falling below strike. So, the higher the strike, the
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/27/2009 for the course FINM 3405 taught by Professor Philipgray during the Three '09 term at Queensland.

Page1 / 10

FINM3405L5 - Black Scholes Option Pricing Formula Lecture 5...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online