Thursday, March 21, 2013

Gamma/Theta Relationship for FX Options

I approach expected option PnL (Profit & Loss) from a holistic approach. Similar to the former post on Expected PnL, i.e. E(PnL) of delta hedged stock options (link), here is the basic estimate for the 24hour E(PnL) for delta neutral FX Options:

Source: Foreign Exchange Derivatives: Advanced Hedging and Trading Techniques
(You're welcome)

Given the following variable definitions:

Sigma: Average Realized Volatility for the life of the trade
S: Underlying FX spot value
Gamma: Option Gamma
r(d): Domestic risk free rate
r(f): Foreign risk free rate
Delta: Option delta
Theta: Option Theta
V: Value of Options (straddles, strangles, etc.)

So how do we use this?

Estimate a RANGE of the coming day's estimated realized vol, and you would find the rough break-even, most-likely points of E(PnL).

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