OPTION PRICING MODEL (BSOP)
QUICK RECAP
BLACK–SCHOLES OPTION PRICING MODEL (BSOP)
HOW DO YOU PRICE AN OPTION PREMIUM?
 Options prices, known as premiums, are composed of the sum of its intrinsic and
time value. Intrinsic value is the price difference between the current
stock price and the strike price. An option's time value or extrinsic value of
an option is the amount of premium above its intrinsic value
 Pricing an option relies on complex mathematical formulas, but the
direct inputs into an option's price include the price of the underlying asset,
the option's strike, time to expiration, interest rates, and implied volatility
 Options are contracts that give option buyers the right to buy or sell a security at
a predetermined price on or before a specified day. The price of an option, called
the premium, is composed of a number of variables. Options traders need to be
aware of these variables so they can make an informed decision about when to
trade an option.
 When investors buy options, the biggest driver of outcomes is the price
movement of the underlying security or stock.
 Call option buyers of stock options need the underlying stock price to rise,
whereas
 Put option buyers need the stock's price to fall.
KEY TERMS
 Options prices, known as premiums, are composed of the sum of its intrinsic and
time value.
 Intrinsic value is the price difference between the current stock price and the
strike price.
 An option's time value or extrinsic value of an option is the amount of premium
above its intrinsic value.
 Time value is high when more time is remaining until expiry since investors have a
higher probability that the contract will be profitable.
 A buyer of an equity call option would want the underlying stock price to be
higher than the strike price of the option by expiry. On the other hand, a buyer of
a put option would want the underlying stock price to be below the put option
strike price by the contract's expiry.
 For example, let's say an investor owns a call option on a stock that is currently
trading at $59 per share.
 The strike price of the option is $55, and the option premium is $5. Because the
stock price is currently $4 more than the option's strike price, then $4 of the $5
premium is comprised of intrinsic value.
 N(d1) is the probability of stock price S>X the exercise price.It is nothing but a
cumulative normal distribution values we find for one tailed tests using z values. It
can be found by calculating area to the right of d1
BLACK–SCHOLES OPTION PRICING MODEL (BSOP)
D1 & D2
 N(d1) is the factor by which the discounted expected value of future receipt of
the stock exceeds the current value of the stock.
 N(d2) is a statistical measure (normal distribution) corresponding to the
probability that the call option will be exercised at expiration.
IMPORTANT POINTS TO NOTE
 Pa is shown in present value terms but Pe is not discounted back to a present value (this
is because in the first formula shown it is multiplied to e–rt which is a form of discount
factor)
 r is the risk-free rate not the cost of capital of the company
 t is the time to expiry of the option, not of the project
 s is standard deviation, you may have to calculate this as the square root of the variance
BLACK–SCHOLES OPTION PRICING MODEL (BSOP)