SOCR EduMaterials Activities ApplicationsActivities BlackScholesOptionPricing
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== Black-Scholes option pricing model - Convergence of binomial == | == Black-Scholes option pricing model - Convergence of binomial == | ||
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+ | * '''Description''': You can access the Black-Scholes applet at http://www.socr.ucla.edu/htmls/app/ . | ||
* Black-Scholes option pricing formula: <br> | * Black-Scholes option pricing formula: <br> | ||
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* The snapshot below from the SOCR Black Scholes Option Pricing model applet shows the path of the stock. | * The snapshot below from the SOCR Black Scholes Option Pricing model applet shows the path of the stock. | ||
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+ | <center>[[Image: Christou_black_scholes.jpg|600px]]</center> |
Revision as of 15:53, 3 August 2008
Black-Scholes option pricing model - Convergence of binomial
- Description: You can access the Black-Scholes applet at http://www.socr.ucla.edu/htmls/app/ .
- Black-Scholes option pricing formula:
The value C < math > ofaEuropeancalloptionattime < math > t = 0 is:
Where,
S_{0} Price of the stock at time t = 0
E Exercise price at expiration
r Continuously compounded risk-free interest
σ Annual standard deviation of the returns of the stock
t Time to expiration in years
Φ(d_{i}) Cumulative probability at d_{i} of the standard normal distribution N(0,1)
- Binomial convergence to Black-Scholes option pricing formula:
The binomial formula converges to the Black-Scholes formula when
the number of periods n is large. In the example below we value the call option using the binomial formula for different values of n and also using the Black-Scholes formula. We then plot the value of the call (from binomial) against the number of periods n. The value of the
call using Black-Scholes remains the same regardless of n. The data used for this example are:
, , R_{f} = 0.05, σ = 0.30,
Days to expiration = 40.
- For the binomial option pricing calculations we divided the 40 days into intervals from 1 to 100 (by 1).
- The snapshot below from the SOCR Black Scholes Option Pricing model applet shows the path of the stock.