Risk Management for Derivatives Case Solution And Analysis, HBR Case Study Solution & Analysis of Harvard Case Studies

Delta

Delta as a measure of risk measures that in case the price of an underlying asset will change then how much it will change the value of financial derivative instruments and these instruments consist of an option, forward or future contracts and this price change is measured using delta, which incorporates the time period it comprises of for changes in price of an underlying asset. The Delta for a long position of one share of stock is the simplest Delta. For example, $1 change in stock price result with the change in a $1 value and the Delta is 1 in this scenario, which will change the long position with change in a value of $1. After knowing that, how much the change will take place in the value of the position in a stock, options, forward contracts and future contract will be changed within the given price limits for an underlying value of an asset. This information will be used for the hedging of a risk for an underlying value of an asset because of this hedging using the Delta known as “Delta hedging”. The formula for calculating the Delta hedging is the Black Scholes Model formula, which is altered for the Delta hedging.

Symbols in this formula are defined as follows:

= Delta Call

¶= Partial Difference

S= current stock price

T= time to exercise the option

K= option strike price

r = risk free rate

e = exponential term

σ = standard deviation

Ln = natural log

Gamma

Gamma is used for measuring the Delta and is the rate of change in Delta. It describes that changes in prices is due to changes in the Delta and these changes are due to changes in the rate of Delta, which is known as Gamma. For the option pricing model, the Delta is not higher within two Delta representations until one of Delta’s Gamma is higher. If the Gamma of the Delta is higher from two Delta values then it means that the Delta, which has the higher Gamma is more volatile than the other Delta.

Vega

Vega is another measurement factor, which defines the risk relationship between price and return. It measures the sensitivity of an option changes with respect to the volatility of an underlying value of assets. Vega also represents the movement in prices of an underlying asset.

Rho

Rho is the rate at which the value of a derivative will change with respect to a change in the risk free rate and it measures the sensitivity of an option with respect to the change in the interest rate.

Theta

Theta measures changes in prices of an underlying option with respect to the time and it is the deterministic factor.

CONCLUSION

In the above analysis, the examination is made on the five different factors that determine and measure the risk that how an option value can be changed with the given change in any one factor. These factors include: Delta, Gamma, Vega, Rho and Theta. These factors changed randomly over the period of given time and these random changes and these factors have on the value of an option for a portfolio of those investors, who hold these portfolios. These risks can be hedged by using one of these factors. Except the Theta, all other factors will be changed with respect to the given time period and with respect to exercise prices that these factors possess on a individual basis. On the other hand, Theta is the only factor that can be determined and that is not the risk factor itself.....................................

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