Sunday, June 19, 2011

first lessons on option delta

I feel delta is the #1 most important greek for a new guy trying to understand option valuation sensitivities.

If you are long or short any security, then you want to monitor your sensitivity to a few key variables. For fixed income positions, you want to monitor sensitivity to IR and credit rating change, among others. For FX positions, you want to monitor sensitivity to IR of multiple currencies...For option positions, you monitor
* (vega) volatility changes. The underlier can exhibit very different volatility from Day 1 to Day 2.
* (delta) underlier price
* (theta) speed of decay
* since delta is such a important thing to watch, you also want to monitor gamma, i.e. how fast your delta changes in response to underlier appreciations.

For a typical option's valuation, sensitivity to underlier is the biggest sensitivity. To trade volatility, you first need to insulate yourself from directional changes. Call it direction-neutral or direction-indifferent. I was told in most cases 0 delta won't "happen to us", so we need to calculate or design our trades so portfolio has 0 delta. Note you get zero delta only at a particular spot price of the underlier. When underlier moves, your portfolio delta won't stay zero.

To learn basic option trading, First a student needs a good grasp over option payoff at expiration. Actually non-trivial. Even for a basic call option, there is a payoff graph like a hockey stick. We need to understand the payoff graph of all 4 basic positions + payoff graph of basic strategies like protective put. Also PCP.

A more realistic graph is portfolio pnl at expiration. "Portfolio pnl" includes the cash you paid/received (realized) in addition to unrealized PnL. In this case, hockey stick crosses x-axis, which is completely realistic. It means your portfolio pnl can be positive or negative depending on the at-expiration price of underlier. Premium cost is a very practical consideration, so it's naive to ignore it in the payoff diagram. Prefer portfolio-PnL.

Next graph or curve[1] is {{ option valuation vs spot price }} i.e. option valuation/premium relative to underlier spot price. Obviously option premium is priced by each trader's pricing engine taking inputs of strike price, time to expiration, vol etc, but here we need to hold all other parameters constant and focus on spot price's effect on option MV. This is how to get the curve. Within this simplified context, we need to
- compare all the basic strategies
- PCP
- know the difference of ITM vs OTM
- know how a basic call's curve depends on vol. We can plot the curve for different vol values

Lastly, Delta is treated like a soft market data on option MV. The slope of the curve in [1] is Gamma. Charm is also a derivative of delta.

Practical usage of delta? Delta is used in delta hedging and delta-neutral trading.

For a typical option's price, sensitivity to underlier is the biggest sensitivity. Therefore delta overshadows vega, theta and rho. But Delta is definitely not the only important greek. In fact, vol is probably the most important factor in option pricing, so vega is rather important.

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http://www.linkedin.com/in/tanbin