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OPTIONS TRADING

Volatility Smiles and Black Swans

options trading volatility smiles black swans

From our previous articles we know that an essential parameter when pricing options is the volatility. The volatility is a measure of the price fluctuation around an average trend movement. In this article we will look at the effect of varying volatility and extreme events on the pricing of options.

In our article about pricing we recall that the standard option pricing tool is the Black Scholes model.  However, the model does not make a correct assumption about the market as it uses a constant volatility across time.  As the recent credit crisis has shown this appears far from true.  The market switched between regimes of quiet action before the credit crisis to high volatility seen in the credit crisis or even extreme moves in the case of currency pegs being broken or sovereign default.  These scenarios need to be priced into the options across strike and maturity. The market uses the Black Scholes model for pricing but does this by varying the volatility parameter for different options.

The at-the-money strike, placed around the current spot level, will usually trade with the lowest volatility parameter. This reflects the fact that if the spot price stays in the vicinity of the at-the-money strike the volatility is low. Furthermore, if the volatility should increase the spot most likely will have moved, resulting in the option having become far out-of-the-money and thus worthless or moved far in-the-money resulting in the option price being equal to a spot position with inception at the strike. That is, the volatility risk will have disappeared. The further we move away from the at-the-money point the higher the probability that we have moved into a higher volatility regime and therefore the volatility is quoted higher. Looking at the volatility as a function of the strike price, we get a curve resembling a smile, see Figure 1, and as consequence we refer to this as the volatility smile of a specific currency pair and tenor.

options trading volatility smiles black swans volatility smile

The smile is, of course, different for different currency pairs and tenors. Some smiles are evenly distributed on both the put and the call side while others are skewed to one side. A skew indicates that the market sees an increased likelihood of a stampede on that side of the at-the-money strike. This could, for an example, be in a currency pair used for carry trading. A rise in the funding currency might force liquidation and a subsequent strong move with high volatility.

To describe the smile the FX market has adopted the standard of quoting the strangle/butterfly and the risk reversal strategy at certain strikes compared to the at-the-money strike. The strikes used will usually be based on the delta (the sensitivity of the option price to a move in the spot price). The most traded delta is the 25 delta. That is the strike where the out-of-the-money option has a delta of 25%. The strangle, see Figure 2, deals with two long positions on each wing and thus represent the average price at these wing points above the at-the-money level in volatility terms. (The option market referrers to each side of the at-the-money as wings. The put wing is where the puts are out-of-the-money. That is, the strikes are below at-the-money. The call wing is the opposite side.) The strangle quote can be seen as an expression of the steepness of the smile, see Figure 1. The risk reversal, see Figure 3, is the ombination of being long a call and short a put and thus represents the difference in price between the two wings. The risk reversal quote can be seen as an expression of the skewness of the smile, see Figure 1.

Š¾ptions trading volatility smiles black swans payoff function strangle

An option trader can use the smile quotes both to understand the Market’s view on a specific currency pair and to trade against it. The strangle deals in particular with the volatility and is non-directional. Therefore, it is best used as a gamma scalping strategy, as described in the previous article. That is going long the strangle and delta hedging in anticipation of a higher volatility regime and getting a higher leverage than simply trading the at-the-money. Or one can short the wings if the market is overpricing the regime change risk. The risk reversal on the other hand always becomes a directional trade, giving the trader a long gamma position on the one side and a short one on the other side. For example, one could be of the opinion that the market is overdoing the downside risk in the EURUSD. For example at the writing of this article there is a skew that favours a weaker EUR stronger USD and therefore, one might consider going long the risk reversal. The deal will obviously make money if the EUR starts to rally. However, the deal could also be made profitable by the spot price going nowhere, in which case the put leg would most likely start to fall in price, or the spot might fall at a slower rate than the volatility suggested by the put leg thus opening up for a gamma scalping strategy by delta hedging the further fall in the spot. The option strategy thus leaves more opportunities for a profitable trade than the simple spot position.

To describe the smile the FX market has adopted the standard of quoting the strangle/butterfly and the risk reversal strategy at certain strikes compared to the at-the-money strike. The strikes used will usually be based on the delta (the sensitivity of the option price to a move in the spot price). The most traded delta is the 25 delta. That is the strike where the out-of-the-money option has a delta of 25%.

The strangle, see Figure 2, deals with two long positions on each wing and thus represent the average price at these wing points above the at-the-money level in volatility terms. (The option market referrers to each side of the at-the-money as wings. The put wing is where the puts are out-of-the-money. That is, the strikes are below at-the-money. The call wing is the opposite side.) The strangle quote can be seen as an expression of the steepness of the smile, see Figure 1. The risk reversal, see Figure 3, is the combination of being long a call and short a put and thus represents the difference in price between the two wings. The risk reversal quote can be seen as an expression of the skewness of the smile, see Figure 1. An option trader can use the smile quotes both to understand the Market’s view on a specific currency pair and to trade against it. The strangle deals in particular with the volatility and is non-directional. Therefore, it is best used as a gamma scalping strategy, as described in the previous article. That is going long the strangle and delta hedging in anticipation of a higher volatility regime and getting a higher leverage than simply trading the at-the-money. Or one can short the wings if the market is overpricing the regime change risk. The risk reversal on the other hand always becomes a directional trade, giving the trader a long gamma position on the one side and a short one on the other side. For example, one could be of the opinion that the market is overdoing the downside risk in the EURUSD. For example at the writing of this article there is a skew that favours a weaker EUR stronger USD and therefore, one might consider going long the risk reversal. The deal will obviously make money if the EUR starts to rally. However, the deal could also be made profitable by the spot price going nowhere, in which case the put leg would most likely start to fall in price, or the spot might fall at a slower rate than the volatility suggested by the put leg thus opening up for a gamma scalping strategy by delta hedging the further fall in the spot. The option strategy thus leaves more opportunities for a profitable trade than the simple spot position.

options trading volatility smiles black swans payoff function risk reversal

The price risk of changes in the volatility regime is captured by the quotes at the delta points. However, as the delta describes the possibility of the market moving to a certain strike in the Black Scholes world, these are not good at describing extreme events. The point here is that such events would either require a huge volatility to fit in the Black Scholes world or they would simply have zero probability and thus no value. Therefore, these options on Black Swans will often be priced in pip terms, where each pip above zero can be interpreted as the market seeing a risk of the currency making an extreme move to that particular strike. Shorting these options will probably lead to nice little profit, most of the time. However should push come to shove and the option becomes in-the-money the outcome will most likely be catastrophic, as the notion of a normal functioning market with good liquidity is probably farfetched and thus hedging opportunities would be small. Options of this calibre should thus only be viewed as pure bets on extreme events.

Steffen Gregersen