Page 119 - DMGT513_DERIVATIVES_AND_RISK_MANAGEMENT

Derivatives & Risk Management

Notes

Task Consider a European call option on a stock when there are ex-dividend dates in two
months and five months. The dividend on each ex-dividend date is expected to be $ 0.5.
The current price is $ 40, the exercise price is $40, the stock price volatility is 30% per
annum, the risk free rate of interest is 9% per annum, and the time to maturity is six
months.

Self Assessment

State the following are true or false:
11. In finance, the binomial options pricing model provides a generalisable numerical method
for the valuation of options.
12. The Black and Scholes Model was first proposed by Cox, Ross and Rubinstein (1979).
13. The fundamental insight of Black and Scholes is that the put option is implicitly priced if
the stock is traded.
14. The Black-Scholes formula is a mathematical formula for the theoretical value of so-called
European put and call stock options that may be derived from the assumptions of the
model.
15. The binomial tree represents different possible paths that may be followed by the stock
price over the life of the option.

8.4 Summary

 The price of an option contract is that amount which is paid by the option buyer to the
option seller. This is otherwise, known as option premium.

 The different factors or determinants which effect option prices are Current Stock Price,
Exercise Price, Volatility, Risk free Interest Rates, Cash Dividends and Time to Expiration.
 To better understand the significance and option pricing techniques, we have to go through
two important models of option valuation like Black-Scholes model and Binomial model.
 This unit also discusses at large the Put-Call parity under the 'with dividend' and 'no
dividend' model.
 Put-call parity is a classic application of arbitrage-based pricing – it does not instruct us on
how to price either put or call options, but it gives us an iron law linking the two prices.

 The put-call parity states that the difference in price between a call-option and a put-
option with the same terms should equal the price of the underlying asset less the present
discounted value of the exercise price.
 In finance, the binomial options pricing model provides a generalisable numerical method
for the valuation of options.

 The binomial model was first proposed by Cox, Ross and Rubinstein (1979).
 The Black-Scholes model, often simply called Black-Scholes, is a model of the varying
price over time of financial instruments, and in particular stock options.

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