Question

Suppose you use Black-Scholes to value a warrant. Will your valuation be too high or too low? Explain why.

Answer 1

Answer:

Black- Scholes:

Black-Scholes is a pricing model used to determine the fair price or theoretical value for a call or a put option based on six variables such as volatility, type of option, underlying stock price, time, strike price, and risk-free rate. The quantum of speculation is more in case of stock market derivatives, and hence proper pricing of options eliminates the opportunity for any arbitrage. There are two important models for option pricing – Binomial Model and Black-Scholes Model. The model is used to determine the price of a European call option, which simply means that the option can only be exercised on the expiration date.

Black-Scholes pricing model is largely used by option traders who buy options that are priced under the formula calculated value, and sell options that are priced higher than the Black-Schole calculated value (1).

The formula for computing option price is as under (2):

Call Option Premium C = SN(d1) - Xe- rt N(d2)

Put Option Premium P = Xe–rT N (–d2) – S0 N (-d1)

Warrants:

Warrants are financial derivatives that give the holders the rights, but not the obligation, to purchase or sell a certain number of underlying assets at a given strike price at a given exercise date. At the exercise date, the holders of the contracts can either exercise the warrants or let the warrants expire. Warrants are relatively new in the Malaysian market. Only recently that warrants are seen as leveraging tools for investments; hence gained its popularity as one of many high return investment tools. Pricing financial derivatives is a fundamental feature in tradings. Pricing warrants is very important as investors need to compute the value of each traded merchandise as accurate as possible to avoid losses. Arbitrage opportunities may appear when there exists a bias in pricing warrants. Warrants and options have several common features such as the underlying asset, exercise price and exercise date. Nevertheless, there exists a difference between warrants and options, such as the dilution effect.

Conclusion:

This implies that the dilution adjustment to the BS model improves the accuracy in estimating the prices for warrants and shows that warrant is overpriced when the volatility is too high and is under-priced when the volatility is too low. Therefore, a possible future work is to price warrants in a model that incorporates stochastic volatility.