# Low Exercise Price Option

A Low Exercise Price Option (LEPO) is an Australian Stock Exchange traded option with a low exercise price that was specifically designed to be traded on margin. It is a European style call option with a low exercise price of $0.01 and a contract size of 1000 shares to be delivered on exercise. The premium is close to the whole share price, and a trader only posts margin, not the full price. Both the buyer and the seller are margined, all positions are marked-to-market daily. LEPOs work like a futures contract. ## Contents ## History The Australian Stock Exchange started listing LEPO exchange traded options in 1995 to allow traders to trade underlying shares on margin. ## Differences from standard options Several important differences distinguish LEPOs from standard exchange-traded options, and these differences have important implications for the pricing of LEPO. • The buyer of a LEPO does not pay the full amount of the premium upfront. • Both buyer and seller of LEPOs involve ongoing margin payments. • The buyer of a LEPO does not receive dividends or obtain voting rights on the underlying shares until the shares are transferred after exercise. • LEPOs are only available as call options. • LEPOs have a very low exercise price and a high premium close to the initial value of the underlying shares. • LEPOs have only one exercise price per expiry month. LEPOs may be over either shares or an index. ## 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.

$L _ {0, 1} = S _ 0 e ^ {r (n/365)} - D e ^ {r(n-y)/365} - X$

where:

• $L _ {0, 1}$ = price of LEPO contract entered into at time 0 for delivery at time 1;
• $S _ 0$ = 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:

$L_{0, 1} = [S _ 0 N(d _ 1) - X e ^ {-rn/365}N(d _ 2)] e ^{rn/365}$

where:

N(d) is cumulative probability distribution function for a standard normal distribution.

$d _ 1 = \dfrac {\ln(S _ 0/X) + (r + {\sigma ^ 2} / 2)(n/365) } { \sigma \sqrt { n/365 } }$
$d _ 2 = d _ 1 - \sigma \sqrt { n/365 }$

For a LEPO an underlying price $S_0$ is very big compare to exercise price X. Because of that $N(d_1)$ is very close to 1, with insignificant difference. Thus LEPO price per Black–Scholes formula (without dividend) is

$L_{0, 1} = S_0 e^{rn/365} - X$

and it matches our previous formula.

## References

1. Stephen A. Easton, Sean M. Pinder “The Pricing of Low Exercise Price Options” http://www.agsm.edu.au/eajm/9812/pdf/easton.pdf
2. Low Exercise Price Options Explanatory Booklet, ASX http://www.asx.com.au/products/pdf/UnderstandingLEPOs.pdf