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What is Marking to Market and How Does it Affect Risk Management in Derivatives Trading?

Short answer

Marking to market means valuing an instrument at the price at which it is currently trading in the market. If you buy an option because you believe it is undervalued then you will not see any profit appear immediately, you will have wait until the market value moves into line with your own estimate. With an option this may not happen until expiration. When you hedge options you have to choose whether to use a delta based on the implied volatility or your own estimate of volatility. If you want to avoid fluctuations in your mark-to-market P&L you will hedge using the implied volatility, even though you may believe this volatility to be incorrect.

Example

A stock is trading at $47, but you think it is seriously undervalued. You believe that the value should be $60. You buy the stock. How much do you tell people your little 'portfolio' is worth? $47 or $60? If you say $47 then you are marking to market, if you say $60 you are marking to (your) model. Obviously this is open to serious abuse and so it is usual, and often a regulatory requirement, to quote the mark-to-market value. If you are right about the stock value then the profit will be realized as the stock price rises. Patience, my son.

Long answer

If instruments are liquid, exchange traded, then marking to market is straightforward. You just need to know the most recent market-traded price. Of course, this doesn't stop you also saying what you believe the value to be, or the profit you expect to make. After all, you presumably entered the trade because you thought you would make a gain.

Hedge funds will tell their investors their Net Asset Value based on the mark-to-market values of the liquid instruments in their portfolio. They may estimate future profit, although this is a bit of a hostage to fortune.

With futures and short options there are also margins to be paid, usually daily, to a clearing house as a safeguard against credit risk. So if prices move against you, you may have to pay a maintenance margin. This will be based on the prevailing market values of the futures and short options. (There is no margin on long options positions because they are paid for up front, from which point the only way is up.)

Marking to market of exchange-traded instruments is clearly very straightforward. But what about exotic or over-the-counter (OTC) contracts? These are not traded actively, they may be unique to you and your counterparty. These instruments have to be marked to model. And this obviously raises the question of which model to use. Usually in this context the 'model' means the volatility, whether in equity markets, FX or fixed income. So the question about which model to use becomes a question about which volatility to use. With credit instruments the model often boils down to a number for risk of default.

Here are some possible ways of marking OTC contracts.

The trader uses his own volatility. Perhaps his best forecast going forward. This is very easy to abuse, it is very easy to rack up an imaginary profit this way. Whatever volatility is used it cannot be too far from the market's implied volatilities on liquid options with the same underlying.

Use prices obtained from brokers. This has the advantage of being real, tradeable prices, and unprejudiced. The main drawback is that you can't be forever calling brokers for prices with no intention of trading. They get very annoyed. And they won't give you tickets to Wimbledon anymore.

Use a volatility model that is calibrated to vanillas. This has the advantage of giving prices that are consistent with the information in the market, and are therefore arbitrage free. Although there is always the question of which volatility model to use, deterministic, stochastic, etc., so 'arbitrage freeness is in the eye of the modeller. It can also be time consuming to have to crunch prices frequently.

One subtlety concerns the marking method and the hedging of derivatives. Take the simple case of a vanilla equity option bought because it is considered cheap. There are potentially three different volatilities here: implied volatility; forecast volatility; hedging volatility. In this situation the option, being exchange traded, would probably be marked to market using the implied volatility, but the ultimate profit will depend on the realized volatility (let's be optimistic and assume it is as forecast) and also how the option is hedged. Hedging using implied volatility in the delta formula theoretically eliminates the otherwise random fluctuations in the mark-to-market value of the hedged option portfolio, but at the cost of making the final profit path dependent, directly related to realized gamma along the stock s path.

By marking to market, or using a model-based marking that is as close to this as possible, your losses will be plain to see. If your theoretically profitable trade is doing badly you will see your losses mounting up. You may be forced to close your position if the loss gets to be too large. Of course, you may have been right in the end, just a bit out in the timing. The loss could have reversed, but if you have closed out your position previously then tough. Having said that, human nature is such that people tend to hold onto losing positions too long on the assumption that they will recover, yet close out winning positions too early. Marking to market will therefore put some rationality back into your trading.

References and Further Reading

Wilmott, P 2006 Paul Wilmott on Quantitative Finance, second edition. John Wiley & Sons Ltd

 
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