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When a trader gets conclusion of the volatility is being underestimated (via volatility cone or some other technology), actually there are multiple ways for his trading. (Let's assume the underlying instrument is equity). 1. Long an option and hedge the delta, to gain from the rallying of volatility. 2. Long straddle strategy to gain from the stock price movement. 3. Long gamma strategy to gain from the stock price movement.

Of course there are more strategies but I just listed these 3 to make the discussion simple and clearer. Let's assume the volatility does rally as expected. For #1, it makes money from option price rallying as the higher volatility. (Here the volatility is defined as Standard Deviation of stock log returns) For #2, it makes money from movement of stock price. (Movement should exceed the profit-loss boundary of straddle. E.g. 87.0-95.0) For #3, it makes money from movement of stock price. (Movement should cover the time decay of option)

The #2 and #3 are equivalent to #1 to some extent, as the higher volatility also means the larger price movement. But they are still not exactly same. When vol rallies 12%, #1 profits, however maybe the stock price movement can not reach the profit-loss boundary for #2 or can not cover the time decay for #3. Option trading is complex and traders have to using math model for risk measurement (and pricing). And seems the models for option are almost based on volatility.

Question 1: How to measure the risk of option strategies like #2 and #3. (I mean the pre-check of risk before trading, not calculating Var at end of a trading day). The models focus on stock volatility could not measure the stock price movement exactly I think, like mentioned above.

Another question is about the risk management after trading. Var is usually used for the portfolio risk management, but option trading has more greeks explored than other trading like cash equity. In our example the main risk of #3 is theta (time decay) risk.

Question 2: So is there any other specific method/model/formula to measure risk for option trading against greeks (like theta in #3) apart from Var? (Some institutions like Bank and Market Maker pay more attention to Var maybe because of the regulation like basel II?)

Much appreciate if you could help on these 2 questions of option market practice. Thanks in advance.

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Perhaps you could consider putting the two question into two separate posts. –  Probilitator Mar 1 at 8:07
Thanks Probilitator for editing both title and content. I paste these 2 together as they are a bit dependent. Both based on the scenario examples I listed. –  Patrick Mar 1 at 11:20
I am not working at a trading desk but I think your question really depends on the setting and which instruments you are trading. Also your question seems to point towards model validation and model risk. Ceck out this question: quant.stackexchange.com/questions/176/model-validation-criteria –  Probilitator Mar 1 at 12:04
It is the general question for all the options trading, anyway I edited the post to say equity option, to let question focus on the main point. Actually my question is not same as model validation topic (it is much general), just want to know the difference between models focus on volatility and models price movement in options market practice. (I did not see the latter in papers envn though :( ) Thanks. –  Patrick Mar 1 at 14:44
Why cant you backtest your strategy, by taking a window of stock prices, implied vols, and run it. This is basically historical VaR approach, though you can age your position to incorporate the time effect. If the horizon is long, you will need stock and vol evolution models through time horizon. –  adam Mar 3 at 8:54
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1 Answer 1

Apart from the usual risks measured by Greeks there's risk associated with volatility dynamics. Volatility surface moves with stock movement and is usually dependant on stock price level. This risk is usually modelled by extensions to volatility models that take underlying price into account or stochastic volatility models (e.g. SABR).

The way to do pre-trade risk check would be to analyse Greeks, look at Greeks dynamics with underlying and volatility movement (the so called risk matrix) assuming the shape of volatility surface changes with underlying price movement.

The risk management after putting a position on is the same as pre-trade - follow the same rules and check your risk on time intervals (e.g. every hour) or price movements (e.g. when stock moves more that 1 daily standard deviation).

Lets compare the three strategies:

  • Long OTM call, delta hedged
  • ATM straddle
  • Long OTM call

A long ATM delta-hedged call is equivalent to ATM straddle in every way so I assume you are talking about OTM options in #1. I've picked calls just as example, it's similar with puts.

Long OTM call, delta hedged

With this strategy you can choose optimal gamma-to-vega ratio by picking the strike of OTM call. The strategy will make money from both gamma and vega but will have more exposure to vol surface dynamics compared to straddle. It's very common that such strategy loses money in a rising market due to vol surface dynamics.

ATM straddle

This strategy is similar to the first one but has more chances to make money in a rising market. The profit-loss boundary is only applicable if you intend to hold the position until expiry. The strategy usually profits on large intra-day movements, there's no reason to hold until expiry. Read about gamma scalping for more info.

Long OTM call

This is not a volatility play, it's a directional bet so the risks are very different. Again, losing money in a rising market is not uncommon with this strategy.

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I feel like his mentioned strategy 1 and 3 are the same, though you understood it as a long call. Patrick can you clarify your long call strategy. –  adam Mar 3 at 8:51
Yes 3 is long gamma not long call, just like mentioned in this link Long Gamma. Thed difference between 1 and 3 is, 3 is to build a delta-neutral (long ATM call, short stock) as the inital position, while 1 is to hedge the option call periodically (like daily) to "reblance" it to (near) delta-neutral. I'm not sure if they are actually same in market practice, just learned from papers and internet. Thanks Derenik and Adam. –  Patrick Mar 3 at 13:16
Long ATM call + short stock is a straddle. Your #2 and #3 are exactly the same then in terms of payoff. #1 as you put it now is the classical way to trade volatility. It'd recommend using #1 if you intend to hold to your position for days and #2/#3 for short plays. The difference between #2 and #3 is transaction costs and margin requirements so pick the one that best suits you. –  derenik Mar 4 at 22:54
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