## Foreign Exchange Volatility Trading Models

4.6.1 Volatility trading strategies

Kroner et al. (1995) point out that, since expectations of future volatility play such a critical role in the determination of option prices, better forecasts of volatility should lead to a more accurate pricing and should therefore help an option trader to identify over- or underpriced options. Therefore a profitable trading strategy can be established based on the difference between the prevailing market implied volatility and the volatility forecast. Accordingly, Dunis and Gavridis (1997) advocate to superimpose a volatility trading strategy on the volatility forecast.

As mentioned previously, there is a narrow relationship between volatility and the option price. An option embedding a high volatility gives the holder a greater chance of a more profitable exercise. When trading volatility, using at-the-money forward (ATMF) straddles, i.e. combining an ATFM call with an ATFM put with opposite deltas, results in taking no forward risk. Furthermore, as noted, amongst others, by Hull (1997), both the ATMF call and put have the same vega and gamma sensitivity. There is no directional bias.

If a large rise in volatility is predicted, the trader will buy both call and put. Although this will entail paying two premia, the trader will profit from a subsequent movement in volatility: if the foreign exchange market moves far enough either up or down, one of the options will end deeply in-the-money and, when it is sold back to the writing counterparty, the profit will more than cover the cost of both premia. The other option will expire worthless. Conversely, if both the call and put expire out-of-the-money following a period of stability in the foreign exchange market, only the premia will be lost.

If a large drop in volatility is predicted, the trader will sell the straddle and receive the two option premia. This is a high-risk strategy if his market view is wrong as he might theoretically suffer unlimited loss, but, if he is right and both options expire worthless, he will have cashed in both premia.

### 4.6.2 The currency volatility trading models

The trading strategy adopted is based on the currency volatility trading model proposed by Dunis and Gavridis (1997). A long volatility position is initiated by buying the 1-month

ATMF foreign exchange straddle if the 1-month volatility forecast is above the prevailing 1-month implied volatility level by more than a certain threshold used as a confirmation filter or reliability indicator. Conversely, a short ATMF straddle position is initiated if the 1-month volatility forecast is below the prevailing implied volatility level by more than the given threshold.

To this effect, the first stage of the currency volatility trading strategy is, based on the threshold level as in Dunis (1996), to band the volatility predictions into five classes, namely, "large up move", "small up move", "no change", "large down move" and "small down move" (Figure 4.4). The change threshold defining the boundary between small and large movements was determined as a confirmation filter. Different strategies with filters ranging from 0.5 to 2.0 were analysed and are reported with our results.

The second stage is to decide the trading entry and exit rules. With our filter rule, a position is only initiated when the 1-month volatility forecast is above or below the prevailing 1-month implied volatility level by more than the threshold. That is:

• If Dt < -c, then sell the ATFM straddle where Dt denotes the difference between the 1-month volatility forecast and the prevailing 1-month implied volatility, and c represents the threshold (or filter).

In terms of exit rules, our main test is to assume that the straddle is held until expiry and that no new positions can be initiated until the existing straddle has expired. As, due to the drop in time value during the life of an option, this is clearly not an optimal trading strategy, we also consider the case of American options which can be exercised at any time until expiry, and thus evaluate this second strategy assuming that positions are only held for five trading days (as opposed to one month).18

As in Dunis and Gavridis (1997), profitability is determined by comparing the level of implied volatility at the inception of the position with the prevailing 1-month realised historical volatility at maturity.

It is further weighted by the amount of the position taken, itself a function of the difference between the 1-month volatility forecast and the prevailing 1-month implied volatility level on the day when the position is initiated: intuitively, it makes sense to assume that, if we have a "good" model, the larger |Dt |, the more confident we should be about taking the suggested position and the higher the expected profit. Calling G this gearing of position, we thus have:19

Large down Small down A Small up Large up

No change

### Figure 4.4 Volatility forecasts classification

18 For the "weekly" trading strategy, we also considered closing out European options before expiry by taking the opposite position, unwinding positions at the prevailing implied volatility market rate after five trading days: this strategy was generally not profitable.

19 Laws and Gidman (2000) adopt a similar strategy with a slightly different definition of the gearing.

Profitability is therefore defined as a volatility net profit (i.e. it is calculated in volatility points or "vols" as they are called by options traders20). Losses are also defined as a volatility loss, which implies two further assumptions: when short the straddle, no stop-loss strategy is actually implemented and the losing trade is closed out at the then prevailing volatility level (it is thus reasonable to assume that we overestimate potential losses in a real world environment with proper risk management controls); when long the straddle, we approximate true losses by the difference between the level of implied volatility at inception with the prevailing volatility level when closing out the losing trade, whereas realised losses would only amount to the premium paid at the inception of the position (here again, we seem to overestimate potential losses). It is further assumed that volatility profits generated during one period are not reinvested during the next. Finally, in line with Dunis and Gavridis (1997), transaction costs of 25 bp per trade are included in our profit and loss computations.

### 4.6.3 Trading simulation results

The currency volatility trading strategy was applied from 31 December 1993 to 9 May 2000. Tables 4.3 and 4.4 document our results for the GBP/USD and USD/JPY monthly trading strategies both for the in-sample period from 31 December 1993 to 9 April 1999 and the out-of-sample period from 12 April 1999 to 9 May 2000. The evaluation discussed below is focused on out-of-sample performance.

For our trading simulations, four different thresholds ranging from 0.5 to 2.0 and two different holding periods, i.e. monthly and weekly, have been retained. A higher threshold level implies requiring a higher degree of reliability in the signals and obviously reduces the overall number of trades.

The profitability criteria include the cumulative profit and loss with and without gearing, the total number of trades and the percentage of profitable trades. We also show the average gearing of the positions for each strategy.

Firstly, we compare the performance of the NNR/RNN models with the benchmark GARCH (1,1) model. For the GBP/USD monthly volatility trading strategy in Table 4.3, the GARCH (1,1) model generally produces higher cumulative profits not only in-sample but also out-of-sample. NNR/RNN models seldom produce a higher percentage of profitable trades in-sample or out-of-sample, although the geared cumulative return of the strategy based on the RNN (44-1-1) model is close to that produced with the benchmark model. With NNR/RNN models predicting more accurately directional change than the GARCH model, one would have intuitively expected them to show a better trading performance for the monthly volatility trading strategies.

This expected result is in fact achieved by the USD/JPY monthly volatility trading strategy, as shown in Table 4.4: NNR/RNN models clearly produce a higher percentage of profitable trades both in- and out-of-sample, with the best out-of-sample performance being that based on the RNN (44-5-1) model. On the contrary, the GARCH (1,1) modelbased strategies produce very poor trading results, often recording an overall negative cumulative profit and loss figure.

20 In market jargon, "vol" refers to both implied volatility and the measurement of volatility in percent per annum (see, amongst others, Malz (1996)). Monetary returns could only be estimated by comparing the actual profit/loss of a straddle once closed out or expired against the premium paid/received at inception, an almost impossible task with OTC options.

Table 4.3 GBP/USD monthly volatility trading strategy

1 Threshold = 0.5

Trading days = 21

Table 4.3 GBP/USD monthly volatility trading strategy

1 Threshold = 0.5

Trading days = 21

Sample |

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