Option Pricing Model

1
Option Pricing Model

• Stephen Yan-leung Cheung
• Professor of Finance (Chair)
• Department of Economics and Finance
• City University of Hong Kong
• March 1, 2001

2
Two Main Pricing Models

• Black-Scholes Model
• Binomial Model

3
1. Black-Scholes Model

• Option value is a function of
• Stock price
• Strike price
• Risk-free rate
• Time to maturity of the option
• Volatility
• Dividends expected during the life of the option

4
1. Black-Scholes Model
5
1. Black-Scholes Model

• What is meant by volatility?

• It is the standard deviation of the stock return
  over a period of time.

6
1. Black-Scholes Model

• Take observations P1, P2,Pn over a period,
  where Pi is the closing price of stock

• Stock return (Ri) is the proportionate change

• Ri ln (Pi/Pi-1)
• The historical volatility is the standard
  deviation of Ri (annualized)

7
1. Black-Scholes Model

• Problems

• What is the right period for estimation?

• Should be the most recent period that is
  generally commensurate with the expected option
  life.

8
1. Black-Scholes Model

• Problems

• What is the right interval to calculate the
  stock return?

• For annualized volatility, weekly return should
  be enough.

9
1. Black-Scholes Model

• Problems

• What is the right price to calculate the stock
  return?

• Weekly closing price or weekly highest price.

10
1. Black-Scholes Model

• Problems

• New issues?

• Historical volatility of similar company of the
  same industry.

11
2. Binomial Model

• Another useful popular technique for pricing a
  stock option is binomial pricing model

• Assumption has to be made on the possible changes
  of stock price over the life of the option

• The two methods give similar approximation and
  the same result under some circumstances

12
Biases in the Black-Scholes Model

• Assumptions
• Stock price distribution
• Volatility is constant
• Large jumps in stock price

Empirical result shows these problems seem to be
less pronounced as an options life increases
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
End