Static Hedging of Standard Options PDF Download
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Author: Peter Carr
Publisher:
ISBN:
Category :
Languages : en
Pages : 61
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Book Description
We consider the hedging of options when the price of the underlying asset is always exposed to the possibility of jumps of random size. Working in a single factor Markovian setting, we derive a new spanning relation between a given option and a continuum of shorter-term options written on the same asset. In this portfolio of shorter-term options, the portfolio weights do not vary with the underlying asset price or calendar time. We then implement this static relation using a finite set of shorter-term options and use Monte Carlo simulation to determine the hedging error thereby introduced. We compare this hedging error to that of a delta hedging strategy based on daily rebalancing in the underlying futures. The simulation results indicate that the two types of hedging strategies exhibit comparable performance in the classic Black-Scholes environment, but that our static hedge strongly outperforms delta hedging when the underlying asset price is governed by Merton (1976)'s jump-diffusion model. The conclusions are unchanged when we switch to ad hoc static and dynamic hedging practices necessitated by a lack of knowledge of the driving process. Further simulations indicate that the inferior performance of the delta hedge in the presence of jumps cannot be improved upon by increasing the rebalancing frequency. In contrast, the superior performance of the static hedging strategy can be further enhanced by using more strikes or by optimizing on the common maturity in the hedge portfolio.We also compare the hedging effectiveness of the two types of strategies using more than six years of data on Samp;P 500 index options. We find that in all cases considered, a static hedge using just five call options outperforms daily delta hedging with the underlying futures. The consistency of this result with our jump model simulations lends empirical support for the existence of jumps of random size in the movement of the Samp;P 500 index. We also find that the performance of our static hedge deteriorates moderately as we increase the gap between the maturity of the target call option and the common maturity of the call options in the hedge portfolio. We interpret this result as evidence of additional random factors such as stochastic volatility.
Author: Peter Carr
Publisher:
ISBN:
Category :
Languages : en
Pages : 61
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Book Description
We consider the hedging of options when the price of the underlying asset is always exposed to the possibility of jumps of random size. Working in a single factor Markovian setting, we derive a new spanning relation between a given option and a continuum of shorter-term options written on the same asset. In this portfolio of shorter-term options, the portfolio weights do not vary with the underlying asset price or calendar time. We then implement this static relation using a finite set of shorter-term options and use Monte Carlo simulation to determine the hedging error thereby introduced. We compare this hedging error to that of a delta hedging strategy based on daily rebalancing in the underlying futures. The simulation results indicate that the two types of hedging strategies exhibit comparable performance in the classic Black-Scholes environment, but that our static hedge strongly outperforms delta hedging when the underlying asset price is governed by Merton (1976)'s jump-diffusion model. The conclusions are unchanged when we switch to ad hoc static and dynamic hedging practices necessitated by a lack of knowledge of the driving process. Further simulations indicate that the inferior performance of the delta hedge in the presence of jumps cannot be improved upon by increasing the rebalancing frequency. In contrast, the superior performance of the static hedging strategy can be further enhanced by using more strikes or by optimizing on the common maturity in the hedge portfolio.We also compare the hedging effectiveness of the two types of strategies using more than six years of data on Samp;P 500 index options. We find that in all cases considered, a static hedge using just five call options outperforms daily delta hedging with the underlying futures. The consistency of this result with our jump model simulations lends empirical support for the existence of jumps of random size in the movement of the Samp;P 500 index. We also find that the performance of our static hedge deteriorates moderately as we increase the gap between the maturity of the target call option and the common maturity of the call options in the hedge portfolio. We interpret this result as evidence of additional random factors such as stochastic volatility.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 272
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Book Description
Author: Francesco Adiliberti
Publisher:
ISBN: 9783258062730
Category : Hedging (Finance)
Languages : en
Pages : 337
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Book Description
Author: Emanuel Derman
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This article presents a practical and useful method for replicating or hedging a target stock option with a portfolio of other options. It shows how to construct a replicating portfolio of standard options with varying strikes and maturities and fixed portfolio weights. Once constructed, this portfolio will replicate the value of the target option for a wide range of stock prices and times before expiration, without requiring further weight adjustments. We call this method static replication. It makes no assumptions beyond those of standard options theory. You can use the technique to construct static hedges for exotic options, thereby minimizing dynamic hedging risk and costs. You can use it to structure exotic payoffs from standard options. Finally, you can use it as an aid in valuing exotic options, since it lets you decompose the exotic option into a portfolio of standard options whose market prices and bid-ask spreads may be better known.
Author: Nassim Nicholas Taleb
Publisher: John Wiley & Sons
ISBN: 9780471152804
Category : Business & Economics
Languages : en
Pages : 536
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Book Description
Destined to become a market classic, Dynamic Hedging is the only practical reference in exotic options hedgingand arbitrage for professional traders and money managers Watch the professionals. From central banks to brokerages to multinationals, institutional investors are flocking to a new generation of exotic and complex options contracts and derivatives. But the promise of ever larger profits also creates the potential for catastrophic trading losses. Now more than ever, the key to trading derivatives lies in implementing preventive risk management techniques that plan for and avoid these appalling downturns. Unlike other books that offer risk management for corporate treasurers, Dynamic Hedging targets the real-world needs of professional traders and money managers. Written by a leading options trader and derivatives risk advisor to global banks and exchanges, this book provides a practical, real-world methodology for monitoring and managing all the risks associated with portfolio management. Nassim Nicholas Taleb is the founder of Empirica Capital LLC, a hedge fund operator, and a fellow at the Courant Institute of Mathematical Sciences of New York University. He has held a variety of senior derivative trading positions in New York and London and worked as an independent floor trader in Chicago. Dr. Taleb was inducted in February 2001 in the Derivatives Strategy Hall of Fame. He received an MBA from the Wharton School and a Ph.D. from University Paris-Dauphine.
Author: Jan H. Maruhn
Publisher: Walter de Gruyter
ISBN: 3110208512
Category : Mathematics
Languages : en
Pages : 210
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Book Description
Static hedge portfolios for barrier options are very sensitive with respect to changes of the volatility surface. To prevent potentially significant hedging losses this book develops a static super-replication strategy with market-typical robustness against volatility, skew and liquidity risk as well as model errors. Empirical results and various numerical examples confirm that the static superhedge successfully eliminates the risk of a changing volatility surface. Combined with associated sub-replication strategies this leads to robust price bounds for barrier options which are also relevant in the context of dynamic hedging. The mathematical techniques used to prove appropriate existence, duality and convergence results range from financial mathematics, stochastic and semi-infinite optimization, convex analysis and partial differential equations to semidefinite programming.
Author: Marco Avellaneda
Publisher: World Scientific
ISBN: 9789810246938
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Contains lectures presented at the Courant Institute's Mathematical Finance Seminar.
Author: Marco Avellaneda
Publisher: World Scientific
ISBN: 9789810237899
Category : Business & Economics
Languages : en
Pages : 390
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Book Description
This volume contains lectures delivered at the Seminar in Mathematical Finance at the Courant Institute, New York University. Subjects covered include: the emerging science of pricing and hedging derivative securities, managing financial risk, and price forecasting using statistics.
Author: San-Lin Chung
Publisher:
ISBN:
Category :
Languages : en
Pages : 33
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Book Description
This paper utilizes the static portfolio approach of Derman, Ergener, and Kani (1995) and Carr, Ellis, and Gupta (1998) to hedge and price American options under the Black-Scholes (1973) model and the constant elasticity of variance (CEV) model of Cox (1975). The static hedge portfolio (SHP) of an American option is formulated by applying the value-matching and smooth-pasting conditions at the early exercise boundaries. The numerical results indicate that the pricing efficiency of our static hedging approach is comparable to some recent advanced numerical methods such as Broadie and Detemple's (1996) binomial Black-Scholes method with Richardson extrapolation (BBSR). Furthermore, our static hedging approach provides simple and intuitive derivations of the early exercise boundaries near expiration.
Author: Klaus Bjerre Toft
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Derman, Ergener, and Kani (1994) construct static hedges of barrier options by assuming that local asset return volatility is a function of asset price and time only. However, Dumas, Fleming, and Whaley (1996) find that local volatilities implied from Samp;P 500 index option prices change in a nonpredictable fashion. It is therefore important to determine how sensitive the quality of a static barrier option hedge is to random changes in local volatilities. We investigate this issue by assuming that options are priced according to Heston's (1993) stochastic volatility model, and use these prices to construct static hedges of up and out barrier options. We then identify distributions of cash flows from these hedges by simulating asset price and volatility paths. Our simulations show that static hedges replicate barrier options quite well if the volatility of volatility is moderate or if the barrier option's payoff does not exhibit discontinuities. However, if the payoff on the boundary is noncontinuous, the quality of the static hedge deteriorates rapidly when the volatility of the volatility is large. This happens because a static hedge typically overhedges the volatility exposure of the target barrier option.
