Posts Tagged ‘options’

RISK DETECTION

Monday, October 12th, 2009

This is the risk radar that investors switch off when they buy a company based on perceived reputation. Reputation is used instead as the proxy for risk management. Thus, many investors went into Enron, Worldcom or Equitable Life because they were regarded as good pedigree
companies. Long-Term Capital Management, adorned with a Nobel prize-winner on board, had a total market exposure estimated at $1250 billion against its capital of $800 million.
Many people just want rapid profit, but they do not have a clue about real risk management. Setting an investment project goal with a risk limit is essential; it is not an optional extra. A predefined project by RAMP methodology has goals, expected performance and variance reporting. This puts adverse CEO spotting back on the project agenda.
Finding the company on our corporate AEW radar can warn us that the company is about to “blow”. This organic-based system uses both figures and mathematical techniques, but is more about the manner in which human beings operate. The forensic evidence can be tracked down in audit trails. There are scents given off by CEO sharks associated by red flags alarm signals for indicating weak banks.
There are essential tools to identify weak banks using early warning techniques. This subjects the supervisor’s data on the bank to a stress testing process, of the bank’s expenses, asset quality of portfolio and their funding. Then we can derive a better risk-discounted picture of the earnings, capital and solvency. This is followed by qualitative (note not quantitative) modelling: Qualitative data
Management/board of directors have oversight administration deficiencies; the oversight  committee may not be empowered, or it is too chummy with the CEO.  Risk management has deficiencies in resourcing, empowerment and skills.
Strategic mistakes have been made by the board into the market. Quantitative data
Performance-related rise in declared profits, asset value, sales.  Aggressive growth and expansion strategies.  Sudden and major deterioration in earnings.
Basel II recognises that such operational risk weaknesses cause big problems for the investors. Its AEW10 system also focuses on warning signs in:
Board management quality.  Effectiveness of policies, procedures and planning.  Execution of risk management controls and audits.  Quality of MIS systems and reporting processes.

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American put option

Tuesday, September 22nd, 2009

As we noted earlier, the holder of an American put option may want to exercise it early. For American call options on underlying assets that make no cash payments, however, there is no justification for exercising the option early. If the underlying asset makes a cash payment, such as a dividend on a stock or interest on a bond, it may be justifiable to exercise the call option early.
For American options on futures, it may be worthwhile to exercise both calls and puts
early. Even though early exercise is never justified for American calls on underlying assets that make no cash payments, early exercise can be justified for American call options on futures. Deep-in-the money American call options on futures behave almost identically to the underlying, but the investor has money tied up in the call. If the holder exercises the call and establishes a futures position, he earns interest on the futures margin account. A similar argument holds for deep-in-the-money American put options on futures. The determination of the timing of early exercise is a specialist topic so we do not explore it here.
If the option is on a forward contract instead of a futures contract, however, these arguments are overshadowed by the fact that a forward contract does not pay off until expiration, in contrast to the mark-to-market procedure of futures contracts. Thus, if one exercised either a call or a put on a forward contract early, doing so would only establish a long or short position in a forward contract. This position would not pay any cash until expiration. No justification exists for exercising early if one cannot generate any cash from the exercise. Therefore, an American call on a forward contract is the same as a European call on a forward contract, but American calls on futures are different from European calls on futures and carry higher prices.

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Implied volatility

Tuesday, September 15th, 2009

In a market in which options are traded actively, we can reasonably assume that the market price of the option is an accurate reflection of its true value. Thus, by setting the Black-Scholes-Merton price equal to the market price, we can work backwards to infer the volatility. This procedure enables us to determine the volatility that option traders are using to price the option. This volatility is called the implied volatility.
Unfortunately, determining implied volatility is not a simple task. We cannot simply solve the Black-Scholes-Merton equation for the volatility. It is a complicated function with the volatility appearing several times, in some cases as a*.There are some mathematical techniques that speed up the estimation of the implied volatility. Here, however, we shall look at only the most basic method: trial and error.
Recall the option we have been working with. The underlying price is 52.75, the exercise price is 50, the risk-free rate is 4.88 percent, and the time to expiration is 0.75. In our previous examples, the volatility was 0.35. Using these values in the Black-Scholes- Merton model, we obtained a call option price of 8.619. Suppose we observe the option selling in the market for 9.25. What volatility would produce this price?
We have already calculated a price of 8.619 at a volatility of 0.35. Because the call price varies directly with the volatility, we know that it would take a volatility greater than 0.35 to produce a price higher than 8.619. We do not know how much higher, so we should just take a guess. Let us try a volatility of 0.40. Using the Black-Scholes-Merton formula with a volatility of 0.40, we obtain a price of 9.446. This is too high, so we try a lower volatility. We keep doing this in the following manner:
Volatility    Black-Scholes-Merton Price
So now we know that the correct volatility lies between 0.38 and 0.39, closer to 0.39. In solving for the implied volatility, we must decide either how close to the option price we want to be or how many significant digits we want in the implied volatility. If we choose four significant digits in the implied volatility, a value of 0.3882 would produce the option
price of 9.2500. Alternatively, if we decide that we want to be within 0.01 of the option price, we would find that the implied volatility is in the range of 38.76 to 38.88 percent.
Thus, if the option is selling for about 9.25, we say that the market is pricing it at a volatility of 0.3882. This number represents the market’s best estimate of the true volatility of the option; it can be viewed as a more current source of volatility information than the past volatility. Unfortunately, a circularity exists in the argument. If one uses the Black-Scholes-Merton model to determine if an option is over- or underpriced, the procedure for extracting the implied volatility assumes that the market correctly prices the option. The only way to use the implied volatility in identifying mispriced options is to interpret the implied volatility as either too high or too low, which would require an estimate of true volatility. Nonetheless, the implied volatility is a source of valuable information on the uncertainty in the underlying, and option traders use it routinely.
All of this material on continuous-time option pricing has been focused on options in which the underlying is an asset. Let us take a look at the pricing of options on futures, which will pave the way for a continuous-time pricing model for options on interest rates, another case in which the underlying is not an asset.

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