Taskin: This Assignment Will Solve Problems About Options

Taskin This Assignment You Will Solve Problems About Options Trading

Suppose a stock is currently trading at 100. An at-the-money call with a maturity of three months has the following price and greeks: C = 5.598, Δ = 0.565, Γ = 0.032, Θ = -12.385, V = 19.685, and Ψ = 12.71. Answer the following questions using Excel functions to perform calculations for each scenario, applying the Greek parameters appropriately.

(a) If the stock price moves to S = 101, what is the predicted new option price (using the delta alone)?

(b) If the stock price moves to S = 101, what is the predicted new call delta?

(c) Repeat these questions assuming the stock price moves to S = 98 instead.

(d) If the stock price registers a large jump increase to 120, what is the new call value predicted by the delta alone? By the delta and gamma combined?

(e) Return to the original parameters. If the time to maturity falls by 0.01, what is the new call value predicted by the theta?

(f) Repeat the last question if the time to maturity falls by 0.05.

(g) Return to the original parameters. If the volatility increases by 1%, what is the predicted new value of the call? What if volatility fell by 2%?

(h) Return to the original parameters. If interest rates should rise by 50 basis points, what is the new call value predicted by the rho?

Using your Excel spreadsheet, perform these calculations, ensuring to apply the full computational capabilities of Excel, including formulas for delta, gamma, theta, vega, and rho impacts on the option value.

Paper For Above instruction

Options trading is a complex yet vital component of modern financial markets, offering traders and investors strategic opportunities to hedge, speculate, and diversify their investment portfolios. The effective management and understanding of options require a comprehensive grasp of the Greek parameters—delta, gamma, theta, vega, and rho—which measure the sensitivities of option prices relative to various underlying factors.

In this paper, we analyze several scenarios involving an at-the-money call option, leveraging the Greeks to project the impact of significant changes in the underlying parameters such as stock price movements, time decay, volatility shifts, and interest rate fluctuations. The primary objective is to demonstrate how the Greek parameters enable precise modeling and prediction of how an option's value responds to different market conditions, facilitating optimal decision-making for traders and risk managers.

We commence by examining the immediate effects of stock price changes from the current level of 100 to values of 101 and 98, calculating the expected new option prices based solely on delta, and adjusting the delta accordingly. The linear approximation provided by delta allows capturing the initial sensitivity of an option's price, but it may fall short when large price jumps occur. Therefore, we include gamma in the analysis when assessing the impact of a substantial increase to 120, illustrating the nonlinear effects on option valuation.

The analysis proceeds into the impact of time decay, highlighting how slight reductions in time to maturity (by 0.01 and 0.05) influence the option price through theta. These calculations showcase how options lose value as expiration approaches, an essential consideration for strategies like calendar spreads and hedging.

Next, the focus shifts to the role of implied volatility, where a 1% increase and a 2% decrease are examined using vega. This segment underscores the importance of volatility in options pricing, especially in volatile markets, and demonstrates how vega adjustments can significantly alter expected option values.

Finally, the sensitivities of options to interest rate changes are explored via rho, emphasizing how shifts in prevailing rates can influence call and put premiums. The calculations here provide insights into managing interest rate risk in options portfolios, especially for fixed-income and bond-related derivatives.

Throughout the analysis, Excel's computational power is instrumental in performing precise calculations, utilizing formulas for each Greek and their impact on option pricing. These models help quantify the risks and potential benefits associated with various scenarios, enabling investors to hedge effectively or capitalize on market movements. The integration of these Greek parameters into decision-making demonstrates their vital role in modern options strategies and risk management practices.

References

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