## Working paper series / Johann-Wolfgang-Goethe-Universität Frankfurt am Main, Fachbereich Wirtschaftswissenschaften : Finance & Accounting

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#### Year of publication

- 2004 (3) (remove)

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- Working Paper (3) (remove)

#### Keywords

- Hedging (2)
- Derivat, Wertpapier (1)
- Discretization Error (1)
- Finanzderivat / Hedging / Strategie / Volatilität / Stochastischer Prozess / Theorie (1)
- Incomplete markets (1)
- Model Error (1)
- Optionspreistheorie / Hedging / Stochastischer Prozess / Theorie (1)
- Stochastic Volatility (1)
- Stochastic jumps (1)
- Volatility Risk Premium (1)

- 140
- Is jump risk priced? - What we can (and cannot) learn from option hedging errors : [This version: November 26, 2004] (2004)
- When options are traded, one can use their prices and price changes to draw inference about the set of risk factors and their risk premia. We analyze tests for the existence and the sign of the market prices of jump risk that are based on option hedging errors. We derive a closed-form solution for the option hedging error and its expectation in a stochastic jump model under continuous trading and correct model specification. Jump risk is structurally different from, e.g., stochastic volatility: there is one market price of risk for each jump size (and not just \emph{the} market price of jump risk). Thus, the expected hedging error cannot identify the exact structure of the compensation for jump risk. Furthermore, we derive closed form solutions for the expected option hedging error under discrete trading and model mis-specification. Compared to the ideal case, the sign of the expected hedging error can change, so that empirical tests based on simplifying assumptions about trading frequency and the model may lead to incorrect conclusions.

- 138
- When are static superhedging strategies optimal? (2004)
- This paper deals with the superhedging of derivatives and with the corresponding price bounds. A static superhedge results in trivial and fully nonparametric price bounds, which can be tightened if there exists a cheaper superhedge in the class of dynamic trading strategies. We focus on European path-independent claims and show under which conditions such an improvement is possible. For a stochastic volatility model with unbounded volatility, we show that a static superhedge is always optimal, and that, additionally, there may be infinitely many dynamic superhedges with the same initial capital. The trivial price bounds are thus the tightest ones. In a model with stochastic jumps or non-negative stochastic interest rates either a static or a dynamic superhedge is optimal. Finally, in a model with unbounded short rates, only a static superhedge is possible.

- 136, Versi
- Can tests based on option hedging errors correctly identify volatility risk premia? (2004)
- Tests for the existence and the sign of the volatility risk premium are often based on expected option hedging errors. When the hedge is performed under the ideal conditions of continuous trading and correct model specification, the sign of the premium is the same as the sign of the mean hedging error for a large class of stochastic volatility option pricing models. We show, however, that the problems of discrete trading and model mis-specification, which are necessarily present in any empirical study, may cause the standard test to yield unreliable results.