conversations.from: human
conversations.value: What could be a title for a book about P>-How, Written, Financial with the genre: Business & Money, Investing?
conversations.from: assistant
conversations.value: A title for this book could be 'Financial Derivatives'
conversations.from: human
conversations.value: the first five paragraphs for this book
conversations.from: assistant
conversations.value: Financial Derivatives
  Professor of Finance, Director, Global Energy Management Institute, Bauer College of Business, University of Houston
  The valuation of options and other contingent claims typically requires the use of computational methods. A variety of computational methods are available. Of these, finite difference methods are among the most well known, most reliable, and most flexible. Finite difference techniques approximate the solution to the partial differential equation that Black, Scholes, and Merton demonstrated that any contingent claim must satisfy when the assumptions they made about stock price dynamics hold. The user of the method can control the accuracy of the approximation, with more accurate approximations requiring greater use of computational resources. Finite difference methods are an essential tool in any derivatives modeler 's kit because they can be adapted to a wide variety of problems, including the valuation of options that permit early exercise and many exotic derivatives.
  This chapter discusses the use of finite difference methods to value contingent claims. I first discuss several basic valuation methods—explicit integration, Monte Carlo integration, and finite difference methods—to put the latter in a more general context. I then set out the common finite difference methods—explicit, implicit, and Crank-Nicolson—used to solve for one-dimensional problems. I then discuss the use of finite difference methods in multidimensional problems, such as options on multiple underlying assets. Finally, I examine the pros and cons of finite difference methods relative to alternative numerical techniques.
  Two basic theoretical frameworks—Martingale methods and the partial differential equation (PDE) approach—motivate two different but equivalent ways of valuing derivative securities. An understanding of these alternative approaches sheds light on the relations between alternative numerical techniques for pricing contingent claims.
  Martingale methods demonstrate that the value of any contingent claim is the expected present value of the claim's cash flows, where the expectation is taken under the "equivalent" probability measure; one example of this equivalent measure is the "risk-neutral" measure where risky securities earn the risk-free rate of return and all cash flows can be discounted at the risk-free rate. When the market is complete (in the sense that the payoffs of any contingent claim can be replicated through a dynamic trading strategy), this equivalent measure is unique.
conversations.from: human
conversations.value: five more paragraphs
conversations.from: assistant
conversations.value: If a hedge fund responds that it may be interested, in which case it requires more detail, the PPD sends the hedge fund a nondisclosure agreement (NDA), which the hedge fund must execute and return before the PPD will send the hedge fund the term sheet and other specifics, including the name of the issuer. The NDA states that the hedge fund will not disclose any of the information being provided to any other party and that it will not act on this information if it chooses not to participate in the private placement.
  The hedge fund sees the convert as a portfolio of instruments. Specifically, it sees a long position in a convert as a combination of a long position in a corporate bond and a long position in a call option on the same corporation's stock. Please see Exhibit 34.1.
  The bond component can be viewed as a bundle of risks. There might be other risks if the convert happens to be callable or putable, but we will assume that it is not.
  The hedge fund actually is only interested in the call option component of the convert and only then if the option can be acquired cheap. This brings us to a fundamental principle of option pricing. The value of an option, as long ago shown by Black and Scholes, is a function of five key variables that can be thought of as the value drivers of the option:
  We can see the current price of the stock, we can see the strike price of the option (at least in the types of options that Black and Scholes were modeling), we can see the time to expiry, and we can see the relevant interest rate. But we cannot see the future volatility of the underlying stock. Thus, when you are trading options, what you are really trading is the one thing you cannot see. You are trading future volatility.
conversations.from: human
conversations.value: Add another sentence about Principal.
conversations.from: assistant
conversations.value: If a hedge fund responds that it may be interested, in which case it requires more detail, the PPD sends the hedge fund a nondisclosure agreement (NDA), which the hedge fund must execute and return before the PPD will send the hedge fund the term sheet and other specifics, including the name of the issuer. The NDA states that the hedge fund will not disclose any of the information being provided to any other party and that it will not act on this information if it chooses not to participate in the private placement. 
  The hedge fund sees the convert as a portfolio of instruments. Specifically, it sees a long position in a convert as a combination of a long position in a corporate bond and a long position in a call option on the same corporation's stock. Please see Exhibit 34. 1. 
  The bond component can be viewed as a bundle of risks. Principal among these are interest rate risk and credit risk. There might be other risks if the convert happens to be callable or putable, but we will assume that it is not. 
  The hedge fund actually is only interested in the call option component of the convert and only then if the option can be acquired cheap. This brings us to a fundamental principle of option pricing. The value of an option, as long ago shown by Black and Scholes, is a function of five key variables that can be thought of as the value drivers of the option:
  We can see the current price of the stock, we can see the strike price of the option (at least in the types of options that Black and Scholes were modeling), we can see the time to expiry, and we can see the relevant interest rate. But we cannot see the future volatility of the underlying stock. Thus, when you are trading options, what you are really trading is the one thing you cannot see. You are trading future volatility.
conversations.from: human
conversations.value: the last four paragraphs
conversations.from: assistant
conversations.value: For the uncertain portion of the portfolio (due to potential fallout), suppose that the manager buys put options on futures to cover $8 million of the pipeline. If Treasury prices fall over the next few weeks or months and rates rise, those loans are likely to close, so she exercises the puts, which give her the right to sell Treasury futures at the price she fixed at the time of purchase. This allows the manager to lock in the futures at that price and install the hedge. The main expense—the hedge cost—is the premium paid to purchase the puts.
  Now let us look at the opposite scenario. If Treasury prices rally and rates drop, the fallout ratio is going to rise, so the $8 million of loans that were covered with the put options drop out of the pipeline. Now there is no need for the hedge, so the manager decides against exercising the options, and they expire worthless. This hedging strategy exposes the manager to some loss, but the loss is limited to the premiums paid to purchase the options. Remember that if she had gone directly into the futures instead of using the options, the fallout would have required her to liquidate the hedge at a higher price than when purchased, and that would have been much more costly than the lost premiums.
  The third scenario is that interest rates do not move at all. In this case, the manager buys the coverage by exercising the put options. In other words, she ends up with the same hedge profile as in the first scenario. The difference is that she loses the options premium and gains the peace of mind that comes from knowing that the hedging strategy is going to work in both rising and falling interest environments.
  Interest rate derivatives come in a wide variety of standardized forms. They can be easily tailored to specific interest rate risk management needs of the user. This chapter has presented an overview of the types of instruments available and examples of their usefulness in managing interest rate risk.