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These are course notes on the application of SDEs to options pricing. The author being partially supported by NSF grant DMS-0739195.
Persistent link: https://www.econbiz.de/10011265235
These notes were originally written for the Stochastic Analysis Seminar in the Department of Operations Research and Financial Engineering at Princeton University, in February of 2011. The seminar was attended and supported by members of the Research Training Group, with the author being...
Persistent link: https://www.econbiz.de/10010781411
Volatility products have become popular in the past 15 years as a hedge against market uncertainty. In particular, there is growing interest in options on the VIX volatility index. A number of recent empirical studies have examine whether there is significantly greater risk premium in VIX...
Persistent link: https://www.econbiz.de/10010976280
We formulate and analyse an inverse problem using derivative prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using Bayesian filtering. However, derivative data can be...
Persistent link: https://www.econbiz.de/10010952257
Persistent link: https://www.econbiz.de/10010751515
We explore the inversion of derivatives prices to obtain an implied probability measure on volatility's hidden state. Stochastic volatility is a hidden Markov model (HMM), and HMMs ordinarily warrant filtering. However, derivative data is a set of conditional expectations that are already...
Persistent link: https://www.econbiz.de/10010600020
Calibrating a trading rule using a historical simulation (also called backtest) contributes to backtest overfitting, which in turn leads to underperformance. In this paper we propose a procedure for determining the optimal trading rule (OTR) without running alternative model configurations...
Persistent link: https://www.econbiz.de/10010931981
This paper is motivated by questions about averages of stochastic processes which originate in mathematical finance, originally in connection with valuing the so-called Asian options. Starting with research of Yor's in 1992, these questions about exponential functionals of Brownian motion have...
Persistent link: https://www.econbiz.de/10005098546
We consider a simple single period economy in which agents invest so as to maximize expected utility of terminal wealth. We assume the existence of three asset classes, namely a riskless asset (the bond), a single risky asset (the stock), and European options of all strikes (derivatives). In...
Persistent link: https://www.econbiz.de/10009208320
We first present a brief but essentially complete survey of the literature on barrier option pricing. We then present two extensions of European up-and-out call option valuation. The first allows for an initial protection period during which the option cannot be knocked out. The second considers...
Persistent link: https://www.econbiz.de/10009279062