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Approximate Hedging With Transaction Costs And Lelands Algorithm In Stochastic Volatility Markets
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Book Synopsis Approximate Hedging with Transaction Costs and Leland's Algorithm in Stochastic Volatility Markets by : Huu-Thai Nguyen
Download or read book Approximate Hedging with Transaction Costs and Leland's Algorithm in Stochastic Volatility Markets written by Huu-Thai Nguyen and published by . This book was released on 2014 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis studies the problem of approximate hedging with constant proportional transaction costs in stochastic volatility models in different situations, using a simpler form for adjusted volatility in the Leland's algorithm. We show that asymptotic properties of hedging error are the same to those in deterministic volatility models and the rate of convergence can be impoved by controlling the model parameter. These can be extended to the case where transaction costs are defined by a general rule. We also show that jumps appear in asset price and/or in stochastic volatility do not affect asymptotic property of hedging error. In the next part, we consider the problem of approximate hedging in the presence of liquidity risks suggested by Cetin, Jarrow and Protter, of which proportional transaction costs models are a particular case. We show that liquidity costs due to smooth supply surves can be ignored using Leland's increasing volatility principle. In the third part, we study the case where the option is written on multiple risky assets. We demonstrate that approximately complete replication can be reached for exchange options using the same parameter suggested by Leland, but it is far from being obvious for other kinds of exotic options. Finally, we propose a simple method to reduce the option price which clearly approaches to the super hedging price in Leland's algorithm. whenever the seller accepts to take a risk defined by a given significance level.
Book Synopsis Approximate Hedging in a Local Volatility Model with Proportional Transaction Costs by : Emmanuel Lepinette
Download or read book Approximate Hedging in a Local Volatility Model with Proportional Transaction Costs written by Emmanuel Lepinette and published by . This book was released on 2013 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Local volatility models are popular because they can be simply calibrated to the market of European options. For such models, we propose a modified Leland method which allows us to approximately replicate a European contingent claim when the market is under proportional transaction costs. The convergence of our scheme is shown by means of a new strategy of proof based on PDEs techniques allowing us to obtain appropriate Greeks estimations.
Book Synopsis Hedging Options Under Transaction Costs and Stochastic Volatility by : Jacek Gondzio
Download or read book Hedging Options Under Transaction Costs and Stochastic Volatility written by Jacek Gondzio and published by . This book was released on 1999 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hedging Options Under Transaction Costs and Stochastic Volatility by : Roy Kouwenberg
Download or read book Hedging Options Under Transaction Costs and Stochastic Volatility written by Roy Kouwenberg and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we consider the problem of hedging contingent claims on a stock under transaction costs and stochastic volatility. Extensive research has clearly demonstrated that the volatility of most stocks is not constant over time. As small changes of the volatility can have a major impact on the value of contingent claims, hedging strategies should try to eliminate this volatility risk. We propose a stochastic optimization model for hedging contingent claims that takes into account the effects of stochastic volatility, transaction costs and trading restrictions. Simulation results show that our approach could improve performance considerably compared to traditional hedging strategies.
Book Synopsis Yet Another Note on the Leland's Option Hedging Strategy with Transaction Costs by : Valeriy Zakamulin
Download or read book Yet Another Note on the Leland's Option Hedging Strategy with Transaction Costs written by Valeriy Zakamulin and published by . This book was released on 2016 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a market with transaction costs the option hedging is costly. The idea presented by Leland (1985) was to include the expected transaction costs in the cost of a replicating portfolio. The resulting Leland's pricing and hedging method is an adjusted Black-Scholes method where one uses a modified volatility in the Black-Scholes formulas for the option price and delta. The Leland's method has been criticized on different grounds. Despite the critique, the risk-return tradeoff of the Leland's strategy is often better than that of the Black-Scholes strategy even in the case when a hedger starts with the same initial value of a replicating portfolio. This implies that the Leland's modification of volatility does optimize somehow the Black-Scholes hedging strategy in the presence of transaction costs. In this paper we explain how the Leland's modified volatility works and show how the performance of the Leland's hedging strategy can be improved by finding the optimal modified volatility. It is not claimed that the Leland's hedging strategy is optimal. Rather, the optimization mechanism of the modified hedging volatility can be exploited to improve the risk-return tradeoffs of other well-known option hedging strategies in the presence of transaction costs.
Book Synopsis On Leland's Option Hedging Strategy with Transaction Costs by : Yonggan Zhao
Download or read book On Leland's Option Hedging Strategy with Transaction Costs written by Yonggan Zhao and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approximate Hedging for Non Linear Transaction Costs on the Volume of Traded Assets by : Romuald Elie
Download or read book Approximate Hedging for Non Linear Transaction Costs on the Volume of Traded Assets written by Romuald Elie and published by . This book was released on 2013 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is dedicated to the replication of a convex contingent claim h(S_1) in a financial market with frictions, due to deterministic order books or regulatory constraints. The corresponding transaction costs rewrite as a non linear function G of the volume of traded assets, with G'(0) > 0. For a stock with Black-Scholes mid-price dynamics, we exhibit an asymptotically convergent replicating portfolio, defined on a regular time grid with h^n trading dates. Up to a well chosen regularization hn of the payoff function, we first introduce the frictionless replicating portfolio of h^n(S^n_1), where Sn is a fictive stock with enlarged local volatility dynamics. In the market with frictions, a proper modification of this portfolio strategy provides a terminal wealth, which converges in probability to the claim of interest h(S_1), as n goes to infinity. In terms of order book shapes, the exhibited replicating strategy only depends on the size 2G'(0) of the bid-ask spread. The main innovation of the paper is the introduction of a 'Leland type' strategy for non-vanishing (non-linear) transaction costs on the volume of traded shares, instead of the commonly considered traded amount of money. This induces lots of technicalities, that we pass through using an innovative approach based on the Malliavin calculus representation of the Greeks.
Book Synopsis Pricing and Hedging Index Options Under Stochastic Volatility by : Saikat Nandi
Download or read book Pricing and Hedging Index Options Under Stochastic Volatility written by Saikat Nandi and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An empirical examination of the pricing and hedging performance of a stochastic volatility (SV) model with closed form solution (Heston 1993) is provided for options on the Samp;P 500 index in which the unobservable time varying volatility is jointly estimated with the time invariant parameters of the model. Although, out-of-sample, the mean absolute pricing error in the SV model is always lower than in the Black-Scholes model, still substantial mispricings are observed for deep out-of-the-money options. The degree of mispricing in different options classes is related to bid-ask spreads on options and options trading volume after controlling for moneyness and maturity biases. Taking into account the transactions costs (bid-ask spreads) in the options market and using Samp;P 500 futures to hedge, it is found that the stochastic volatility model yields lower variance for a minimum variance hedge portfolio than the Black-Scholes model for most classes of options and the differences in variances are statistically significant. The views expressed here are those of the author and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System.
Book Synopsis When You Hedge Discretely by : Artur Sepp
Download or read book When You Hedge Discretely written by Artur Sepp and published by . This book was released on 2015 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the delta-hedging strategy for a vanilla option under the discrete hedging and transaction costs, assuming that an option is delta-hedged using the Black-Scholes-Merton model with the log-normal volatility implied by the market price of the option. We analyze the expected profit-and-loss (P&L) of the delta-hedging strategy assuming the four possible dynamics of asset returns under the statistical measure: the log-normal diffusion, the jump-diffusion, the stochastic volatility and the stochastic volatility with jumps. For all of the four models, we derive analytic formulas for the expected P&L, expected transaction costs, and P&L volatility assuming hedging at fixed times. Using these formulas, we formulate the problem of finding the optimal hedging frequency to maximize the Sharpe ratio of the delta-hedging strategy. Also, we show that the Sharpe ratio of the delta-hedging strategy can be improved by incorporating the price and delta bands for the rebalancing of the delta-hedge and provide analytical approximations for computing the optimal bands in our optimization approach. As illustrations, we show that our method provides a very good approximation to the actual Sharpe ratio obtained by Monte Carlo simulations under the time-based re-hedging. In contrary to Monte Carlo simulations, our analytic approach provide a fast and an accurate way to estimate the risk-reward characteristic of the delta-hedging strategy for real time computations.
Book Synopsis The Effect of Stochastic Volatility on Portfolio Optimization with Transaction Costs by : Scott M. Weiner
Download or read book The Effect of Stochastic Volatility on Portfolio Optimization with Transaction Costs written by Scott M. Weiner and published by . This book was released on 2000 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Hedging and Valuation Under Stochastic Volatility by : Joshua Rosenberg
Download or read book Option Hedging and Valuation Under Stochastic Volatility written by Joshua Rosenberg and published by . This book was released on 1996 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hedging Options in the Incomplete Market with Stochastic Volatility by : Rituparna Sen
Download or read book Hedging Options in the Incomplete Market with Stochastic Volatility written by Rituparna Sen and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We show that it is possible to avoid the discrepancies of continuous path models for stock prices and still be able to hedge options if one models the stock price process as a birth and death process. One needs the stock and another market traded derivative to hedge an option in this setting. However, unlike in continuous models, number of extra traded derivatives required for hedging does not increase when the intensity process is stochastic. We obtain parameter estimates using Generalized Method of Moments and describe the Monte Carlo algorithm to obtain option prices. We show that one needs to use filtering equations for inference in the stochastic intensity setting. We present real data applications to study the performance of our modeling and estimation techniques.
Book Synopsis Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations by : Valeriy Zakamulin
Download or read book Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations written by Valeriy Zakamulin and published by . This book was released on 2008 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the presence of transaction costs the perfect option replication is impossible which invalidates the celebrated Black and Scholes (1973) model. In this chapter we consider some approaches to option pricing and hedging in the presence of transaction costs. The distinguishing feature of all these approaches is that the solution for the option price and hedging strategy is given by a nonlinear partial differential equation (PDE). We start with a review of the Leland (1985) approach which yields a nonlinear parabolic PDE for the option price, one of the first such in finance. Since the Leland's approach to option pricing has been criticized on different grounds, we present a justification of this approach and show how the performance of the Leland's hedging strategy can be improved. We extend the Leland's approach to cover the pricing and hedging of options on commodity futures contracts, as well as path-dependent and basket options. We also present examples of finite-difference schemes to solve some nonlinear PDEs. Then we proceed to the review of the most successful approach to option hedging with transaction costs, the utility-based approach pioneered by Hodges and Neuberger (1989). Judging against the best possible tradeoff between the risk and the costs of a hedging strategy, this approach seems to achieve excellent empirical performance. The asymptotic analysis of the option pricing and hedging in this approach reveals that the solution is also given by a nonlinear PDE. However, this approach has one major drawback that prevents the broad application of this approach in practice, namely, the lack of a closed-form solution. The numerical computations are cumbersome to implement and the calculations of the optimal hedging strategy are time consuming. Using the results of asymptotic analysis we suggest a simplified parameterized functional form of the optimal hedging strategy for either a single option or a portfolio of options and a method for finding the optimal parameters.
Book Synopsis An Approximate Distribution of Delta-Hedging Errors in a Jump-Diffusion Model with Discrete Trading and Transaction Costs by : Artur Sepp
Download or read book An Approximate Distribution of Delta-Hedging Errors in a Jump-Diffusion Model with Discrete Trading and Transaction Costs written by Artur Sepp and published by . This book was released on 2014 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a jump-diffusion model for asset returns with jumps drawn from a mixture of normal distributions and show that this model adequately fits the historical data of the Samp;P500 index. We consider delta-hedging strategy for vanilla options under the diffusion model (DM) and the proposed jump-diffusion model (JDM) assuming discrete trading intervals and transaction costs, and derive an approximation for the probability density function (PDF) of the profit-and-loss (Pamp;L) of the delta-hedging strategy under the both models. We find that, under the log-normal model by Black-Scholes-Merton, the actual PDF of the Pamp;L can be well approximated by the chi-squared distribution with specific parameters. We derive an approximation for the Pamp;L volatility in the DM and JDM. We show that, under the both DM and JDM, the expected loss due to transaction costs is inversely proportional to the square root of the hedging frequency. We apply the mean-variance analysis to find the optimal hedging frequency given the hedger's risk tolerance. Since under the JDM it is impossible to reduce the Pamp;L volatility by increasing the hedging frequency, we consider an alternative hedging strategy, following which the Pamp;L volatility can be reduced by increasing the hedging frequency.
Book Synopsis Hedging Options with Transaction Costs Using Stochastic Control and Machine Learning by : Thishan Hansragh
Download or read book Hedging Options with Transaction Costs Using Stochastic Control and Machine Learning written by Thishan Hansragh and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Deep Hedging written by Hans Buehler and published by . This book was released on 2019 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods.We discuss how standard reinforcement learning methods can be applied to non-linear reward structures, i.e. in our case convex risk measures. As a general contribution to the use of deep learning for stochastic processes, we also show in section 4 that the set of constrained trading strategies used by our algorithm is large enough to ∈-approximate any optimal solution.Our algorithm can be implemented efficiently even in high-dimensional situations using modern machine learning tools. Its structure does not depend on specific market dynamics, and generalizes across hedging instruments including the use of liquid derivatives. Its computational performance is largely invariant in the size of the portfolio as it depends mainly on the number of hedging instruments available.We illustrate our approach by showing the effect on hedging under transaction costs in a synthetic market driven by the Heston model, where we outperform the standard “complete market” solution.This is the "stochastic analysis" version of the paper. A version in machine learning notation is available here "https://ssrn.com/abstract=3355706" https://ssrn.com/abstract=3355706.
Book Synopsis Derivative Pricing and Hedging for Incomplete Markets: Stochastic Arbitrage and an Adaptive Procedure for Stochastic Volatility by : Stephanos C. Panayides
Download or read book Derivative Pricing and Hedging for Incomplete Markets: Stochastic Arbitrage and an Adaptive Procedure for Stochastic Volatility written by Stephanos C. Panayides and published by . This book was released on 2005 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
