Mathematical Modeling in Finance with Stochastic Processes
1.2. OPTIONS AND DERIVATIVES 21 Options are calledin the money,at the moneyorout of the money. An in-the-money option would lead ...
22 CHAPTER 1. BACKGROUND IDEAS 1.2 Intrinsic value of a call option ...
1.2. OPTIONS AND DERIVATIVES 23 the strike priceK, the time to expirationT−twhereTis the expiration time andtis the current tim ...
24 CHAPTER 1. BACKGROUND IDEAS Roughly speaking the volatility of a stock price is a measure of how much future stock price move ...
1.3 Speculation and Hedging (a) Draw the graph of the value of the option contract composed of holding a put option with strike ...
26 CHAPTER 1. BACKGROUND IDEAS Section Starter Question Discuss examples in your experience of speculation. (Example: think of “ ...
1.3. SPECULATION AND HEDGING 27 the investor loses $0.20 on each $2.50 share, for a loss of 8%. These are both standard calculat ...
28 CHAPTER 1. BACKGROUND IDEAS investor loses the whole of the initial investment of $500. If the stock price is above $140 on t ...
1.3. SPECULATION AND HEDGING 29 Example: Hedging with a portfolio with puts and calls Since the value of a call option rises whe ...
30 CHAPTER 1. BACKGROUND IDEAS that the number of stock shares calculated from the hedge ratio is rounded to an integer number o ...
1.3. SPECULATION AND HEDGING 31 Sources The ideas in this section are adapted fromOptions, Futures and other Deriva- tive Securi ...
32 CHAPTER 1. BACKGROUND IDEAS 1.4 Arbitrage Rating Student: contains scenes of mild algebra or calculus that may require guid- ...
1.4. ARBITRAGE 33 Mathematical Ideas The notion of arbitrage is crucial in the modern theory of finance. It is the cornerstone o ...
34 CHAPTER 1. BACKGROUND IDEAS set the price at $390 per ounce (called aforward contract). Suppose that the price for borrowing ...
1.4. ARBITRAGE 35 1.3 A diagram of the cash flow in the gold arbitrage price could ever exist in the first place. In the second ...
36 CHAPTER 1. BACKGROUND IDEAS non-existent as $100 bills lying in the street. It might happen, but we don’t base our activities ...
1.4. ARBITRAGE 37 Modeling of Derivative Securities, by M. Avellaneda and P. Laurence, Chapman and Hall, Boca Raton, 2000, Exerc ...
38 CHAPTER 1. BACKGROUND IDEAS Outside Readings and Links: A lecture on currency arbitrage A link to a youtube video. 1.5 Math ...
1.5 Mathematical Modeling Mathematical Ideas Remember the following proverb: All mathematical models are wrong, but some mathema ...
40 CHAPTER 1. BACKGROUND IDEAS Figure 1.4: The cycle of modeling ...
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