Part A

A 95 strike 3 month put for a current spot at 100 and implied volatility of 30% has theta at -9.9123, a gamma of 0.0239 and a vega of 17.8893. Estimate the breakeven for the stock move in a week or change in time, t, = 0.0198, with zero rates.

Part B

Adjust the Black Merton Scholes PDE for the breakeven in the stock with zero rates, for the presence of vega risk. Now reestimate the breakeven point for the weekly stock move when we expect volatility to rise by a vol point.

PLEASE SHOW WORK ON HOW ANSWER CAME TO BE, PROVIDE FORMULAS.