Bull spread

Abstract: Optimal stopping and mathematical finance are intimately connected since the value of an American option is given as the solution to an optimal stopping problem. Such a problem can be viewed as a game in which we are trying to maximize an expected reward. The solution involves finding the best possible strategy, or equivalently, an optimal stopping time for the game. Moreover, the reward corresponding to this optimal time should be determined. It is also of interest to know how the solution depends on the model parameters. For example, when pricing and hedging an American option, the volatility needs to be estimated and it is of great practical importance to know how the price and hedging portfolio are affected by a possible misspecification.The first paper of this thesis investigates the performance of the delta hedging strategy for a class of American options with non-convex payoffs. It turns out that an option writer who overestimates the volatility will obtain a superhedge for the option when using the misspecified hedging portfolio.In the second paper we consider the valuation of a so-called stock loan when the lender is allowed to issue a margin call. We show that the price of such an instrument is equivalent to that of an American down-and-out barrier option with a rebate. The value of this option is determined explicitly together with the optimal repayment strategy of the stock loan.The third paper considers the problem of how to optimally stop a Brownian bridge. A finite horizon optimal stopping problem like this can rarely be solved explicitly. However, one expects the value function and the optimal stopping boundary to satisfy a time-dependent free boundary problem. By assuming a special form of the boundary, we are able to transform this problem into one which does not depend on time and solving this we obtain candidates for the value function and the boundary. Using stochastic calculus we then verify that these indeed satisfy our original problem.In the fourth paper we consider an investor wanting to take advantage of a mispricing in the market by purchasing a bull spread, which is liquidated in case of a market downturn. We show that this can be formulated as an optimal stopping problem which we then, using similar techniques as in the third paper, solve explicitly.In the fifth and final paper we study convexity preservation of option prices in a model with jumps. This is done by finding a sufficient condition for the no-crossing property to hold in a jump-diffusion setting.

Abstract: The main aim of this study is to analyze the performance of four different options spread strategies on the Indian stock market index, Nifty. These strategies are analyzed using monthly data for the 2007–2018 period. The four strategies used in this analysis are 1) bull call spread, 2) bull put spread, 3) bear call spread, and 4) bear put spread. The results have been analyzed on the basis of profitability (in terms of points earned or lost in Nifty) and monthly success rate. The result shows that bull spread strategies have a higher success rate than the bear spread strategies. Further, the bull call and put spread strategy is found to be profitable while the bear call and put spread strategy is found to produce losses. Comparing both bull spread strategies on the basis of profitability, the bull call spread strategy is shown to be 2.75 times more profitable than the bull put spread strategy. Because of higher profitability, the bull call spread can be used consistently in Nifty. Better return of the bull spread strategies indicates that Nifty exhibits less bearish than bullish behavior while the better performance of bull call spread over bull put spread indicates that the Indian stock market gives excessive return to the investor. For any trader on the Nifty, these findings will be useful for trading. TOPICS:Options, performance measurement, emerging markets

Abstract: Preface. Acknowledgments. PART I Understanding Terms and Theory. CHAPTER 1 Options Basics and Terms. Calls and Puts. Classes and Series. In the Money, Out of the Money, and At the Money. Premium and Time Decay. Intrinsic versus Extrinsic Value. Volatility. CHAPTER 2 Calls and Puts. Call Options. Put Options. CHAPTER 3 Option Theory. Option Pricing Models. Fundamentals of Pricing Models. Types of Pricing Models. Inputs of the Options Pricing Model. Outputs of the Pricing Model. CHAPTER 4 Option Theory and the Greeks. Delta. Gamma. Vega. Theta. Second-Tier Greeks. CHAPTER 5 Synthetic Positions. Defining Synthetics. Synthetic Stock. Synthetic Call. Synthetic Put. PART II Basic Strategies. CHAPTER 6 Introduction to Trading Strategies. Directional Trading Strategies. In-the-Money, Out-of-the-Money, and At-the-Money Options. Leverage and Risk. CHAPTER 7 Covered Call/Buy-Write Strategy. Foundations of the Strategy. Performance in Different Scenarios. Lean. Rolling the Position. Examples. Covered Call/Buy-Write Synopsis. CHAPTER 8 The Covered Put/Sell-Write Strategy. Reviewing Selling Short. Foundations of the Strategy. Performance in Different Scenarios. Lean. Rolling the Position. Examples. Covered Put/Sell-Write Synopsis. CHAPTER 9 The Protective Put Strategy. Foundations of the Strategy. Performance in Different Scenarios. Lean. When to Use the Protective Put Strategy. Examples. Protective Put Synopsis. CHAPTER 10 The Synthetic Put/Protective Call Strategy. Foundations of the Strategy. Performance in Different Scenarios. Lean. When to Use the Protective Call Strategy. Examples. Synthetic Put Synopsis. CHAPTER 11 The Collar Strategy. Foundations of the Strategy. Performance in Different Scenarios. Lean. Examples. Collar Synopsis. PART III Advanced Strategies: Spread Trading, Straddles, and Strangles. CHAPTER 12 Vertical Spreads. Construction of a Vertical Spread. Value and the Vertical Spread. Spread Prices Fluctuate. Factors that Affect Spread Pricing. Rolling the Position. Time Decay and Volatility Trading Opportunities. An Imaginary Spread Scenario. Recap with Special Insights. Examples. Bull Spread Synopsis. Bear Spread Synopsis. CHAPTER 13 Time Spreads. Construction of the Time Spread. Behavior of the Spread. Effects of Stock Price on the Time Spread. Effects of Volatility on the Time Spread. Buyer Risk and Reward. Seller Risk and Reward. Rolling the Position. Concluding Thoughts. Examples. Time Spread Synopsis. CHAPTER 14 The Stock Replacement/Covered Call Strategy (Diagonal Spread). When to Use the Diagonal Spread. Rolling the Position. Conclusion. CHAPTER 15 Straddles. What Is a Straddle? Straddle Scenarios. How It Works. Factors that Affect Straddle Prices. Risks and Rewards. Break-Even, Maximum Reward, and Maximum Risk. Conclusion. Examples. Long Straddle Synopsis. Short Straddle Synopsis. CHAPTER 16 Strangles. What Is a Strangle? Strangle Scenarios. How It Works. Factors that Affect Strangle Prices. Risks and Rewards. Break-Even, Maximum Reward, and Maximum Risk. Conclusion. Examples. Long Strangle Synopsis. Short Strangle Synopsis. PART IV Combination Strategies. CHAPTER 17 The Butterfly. Constructing the Butterfly. Why Use Butterflies? Butterfly and Synthetic Positions. What Will a Butterfly Cost? Butterfly and the Greeks. Iron Butterfly. Long Iron Butterfly. Using the Butterfly. Long Butterfly Synopsis. Short Butterfly Synopsis. CHAPTER 18 The Condor. Long Condor. Short Condor. Why Use Condors?. How It Works. Condors versus Butterflies. Condors and the Greeks. Iron Condors. How Do We Use Condors? Long Condor Synopsis. Short Condor Synopsis. Conclusion. Appendix: Five Trading Sheets. About the Author. Index.

Abstract: We observe that the incentive effects of traditional stock options can be improved by making the option's payoff concave in the region of a high stock price at maturity. To reflect the concave property, we propose two types of executive stock options: a generalized power option and an ordinary bull spread. Under the [Hall and Murphy (): American Economic Review 209‐214, Hall and Murphy () Journal of Accounting and Economics 33: 3‐42] framework, we show that the generalized power option with high concavity and the ordinary bull spread generate greater incentive effects than those of traditional options or the [Bernard, Boyle, and Chen (): The Journal of Derivatives 23: 9‐20] power executive options.