Pricing of Low Exercise Price Options
The current value of a contract is equal to the current price of the underlying share compounded by the risk-free interest rate, less the accumulated value of any dividends, less the exercise price of $0.01.
where:
- = price of LEPO contract entered into at time 0 for delivery at time 1;
- = price of underlying share at time 0;
- r = risk-free rate of return;
- n = number of days until contract maturity;
- D = value of share dividends;
- y = number of days until dividend is paid.
- X = exercise price (equals $0.01);
To prove that above formula is correct, we'll calculate price using Black–Scholes formula. The Black–Scholes formula after modifications to recognize that the premium is paid at the expiry of the contract:
where:
N(d) is cumulative probability distribution function for a standard normal distribution.
For a LEPO an underlying price is very big compare to exercise price X. Because of that is very close to 1, with insignificant difference. Thus LEPO price per Black–Scholes formula (without dividend) is
and it matches our previous formula.
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