FAQs on Derivatives Analysis and Valuation

An embedded derivative is a derivative instrument that is embedded in another contract, called the host contract. The host contract might be a debt or equity instrument, a lease, an insurance contract or a sale or purchase contract. They are a result of financial engineering, though some may arise inadvertently due to market practices and contracting arrangements. There is intentional shifting of risks between the parties. They may cause modification to a contract’s cash flow, if there is any change in specified variable.

A derivative requires to be marked to market through the Income statement. Embedded derivatives are also marked-to-market. This requirement on embedded derivative is designed to ensure that mark-to-market is not avoided by including or embedding a derivative in another contract or financial instrument which is not marked-to-market through the Income statement.

The following are the points of difference between a Future contract and an option contract.

The derivative instruments are the outcome of financial engineering and their value is based on some underlying asset. The underlying may be a share, a commodity or any other asset which has a marketable value which is subject to market risks. The importance of underlying in derivative instruments is as follows:

• • All derivative instruments are dependent on an underlying to have value.
  • The change in value in a forward contract is broadly equal to the change in value in the underlying.
  • In the absence of a valuable underlying asset the derivative instrument will have no value.
  • On maturity, the position of profit/loss is determined by the price of underlying instruments. If the price of the underlying is higher than the contract price the buyer makes a profit. If the price is lower, the buyer suffers a loss.

The following are the assumptions of Black Scholes Model;

1. 1. The option is a European option.
   2. There are no transaction charges.
   3. There are no taxes.
   4. The risk free rate is known and is constant over the life of the option.
   5. Stocks do not pay dividend.
   6. Stock returns are normally distributed over a period of time.
   7. The variance of the return is constant over the life of an option.

The price of an option is a function of spot price, exercise price, time to expiration, risk free rate of return, volatility and dividends. These are explained as follows:

1. 1. Market Price of the underlying asset: Call option is directly related to the spot price so the value of call option increases with rise in spot prices. The put option has inverse relation with the spot price, so its value decreases with increase in spot price.
   2. Exercise price or Strike price (X): Call is inversely related to the strike price and Put is directly related with strike price.
   3. Time to Expiration: The price of both Call and Put are directly related to the time. The longer the maturity, the higher will be the price of options.
   4. Volatility: The price of both Call and Put are directly related to the volatility. The higher the movement in underlying, the higher will be the price of options.
   5. Risk free rate of return: The Call premium is higher with higher rate of interest and vice versa, whereas Put option price is inversely related to the risk free rate of return.
   6. Dividends: if the dividends are receivable before the due date of expiration of an option and the market price is cum-dividends then put option will be higher and call option premium will be lower.

It is the degree to which an option price will move, given a small change in the underlying stock price. A deeply out of money call will have delta very close to zero and a deeply in the money call will have a delta close to 1.

For example, if the delta is 0.1, Re.1 change in underlying will change the value of option by Re. 0.10. If delta is 0.95, a Re.1 change in underlying will change the value of option by Rs. 0.95.

It measures how fast the delta changes for a small change in the underlying stock price. It is the delta of the delta. If a portfolio is hedged using delta-hedge technique, the gamma should be small. A small gamma will not bring much change in the delta and therefore portfolio will not require adjustment.

It measures the sensitivity of option value to change in volatility. Vega indicates an absolute change in option value for a one percentage change in volatility.

It measures the sensitivity of option value to change in interest rate. It is the change in option price given a one percentage point change in the risk-free interest rate. Rho indicates the absolute change in option value for a one percent change in the interest rate.