This set of problems assumes that we have options on a stock with a current value of $50, a volatility = 50%, and a continuously-compounded risk-free rate of 3%.
In the worksheets labeled, "Long Risk Reversal", "Short Risk Reversal", "Bull Spread", etc., I have created VBA functions to calculate Black-Scholes model deltas, gammas, vegas, and taus.
Column G shows the net portfolio value of delta, gamma, vega, and tau.
The change is value of a portfolio, , can be expressed as
Use this information to answer the questions below. The change is value of a
List the net delta, gamma, vega, and tau of a Long Risk Reversal: Short 1 Put(X = 45, T = 0.5), Long 1 Call(X = 55, T = 0.5).
List the net delta, gamma, vega, and tau of a Short Risk Reversal: Long 1 Put(X = 45, T = 0.5), Short 1 Call(X = 55, T = 0.5).
List the net delta, gamma, vega, and tau of a Bull Spread: Long 1 Put(X = 45, T = 0.5), Short 1 Put(X = 55, T = 0.5).
List the net delta, gamma, vega, and tau of a Bear Spread: Short 1 Put(X = 45, T = 0.5), Long 1 Put(X = 55, T = 0.5).
List the net delta, gamma, vega, and tau of a Long Straddle: Long 1 Put(X = 50, T = 0.5), Long 1 Call(X = 50, T = 0.5).
List the net delta, gamma, vega, and tau of a Short Butterfly: Short 1 Call(X = 45, T = 0.5), Long 2 Call(X = 50, T = 0.5)'s, Short 1 Call(X = 55, T = 0.5).
List the net delta, gamma, vega, and tau of a Long Strangle: Long 1 Put (X = 45, T = 0.5), Long 1 Call(X = 55, T = 0.5).
List the net delta, gamma, vega, and tau of a 1: 2 Ratio Call Backspread: Long 1 Call(X = 45, T = 0.5), Short 2 Call(X = 55, T = 0.5)'s.
List the net delta, gamma, vega, and tau of a 1:2 Ratio Backspread: Long 1 Put (X = 55, T = 0.5), Short 2 Put(X = 45, T = 0.5)'s, ,Long 1 Call(X = 55, T = 0.5).
Put you answers in a spreadsheet and put it in your report.