Efficient trinomial trees for local‐volatility models in pricing double‐barrier options

Since their introduction, quanto options have steadily gained popularity. Matching Black–Scholes-type pricing models and, more recently, a fat-tailed, normal tempered stable variant have been established. The objective here is to empirically assess the adequacy of quanto-option pricing models. The validation of quanto-pricing models has been a challenge so far, due to the lack of comprehensive data records of exchange-traded quanto transactions. To overcome this, we make use of exchange-traded structured products. After deriving prices for composite options in the existing modeling framework, we propose a new calibration procedure, carry out extensive analyses of parameter stability and assess the goodness of fit for plain vanilla and exotic double-barrier options.

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Robustness of Delta Hedging for Path-Dependent Options in Local Volatility Models

Journal of Applied Probability ◽

10.1017/s0021900200003594 ◽

2007 ◽

Vol 44 (04) ◽

pp. 865-879 ◽

Cited By ~ 3

Author(s):

Alexander Schied ◽

Mitja Stadje

Keyword(s):

Payoff Function ◽

Hedging Strategy ◽

Local Volatility ◽

Directional Convexity ◽

Volatility Models ◽

Local Volatility Model ◽

Volatility Model ◽

Black Scholes ◽

Delta Hedging ◽

Path Dependent

We consider the performance of the delta hedging strategy obtained from a local volatility model when using as input the physical prices instead of the model price process. This hedging strategy is called robust if it yields a superhedge as soon as the local volatility model overestimates the market volatility. We show that robustness holds for a standard Black-Scholes model whenever we hedge a path-dependent derivative with a convex payoff function. In a genuine local volatility model the situation is shown to be less stable: robustness can break down for many relevant convex payoffs including average-strike Asian options, lookback puts, floating-strike forward starts, and their aggregated cliquets. Furthermore, we prove that a sufficient condition for the robustness in every local volatility model is the directional convexity of the payoff function.

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A unified approach to Bermudan and barrier options under stochastic volatility models with jumps

Journal of Economic Dynamics and Control ◽

10.1016/j.jedc.2017.05.001 ◽

2017 ◽

Vol 80 ◽

pp. 75-100 ◽

Cited By ~ 38

Author(s):

J. Lars Kirkby ◽

Duy Nguyen ◽

Zhenyu Cui

Keyword(s):

Stochastic Volatility ◽

Barrier Options ◽

Unified Approach ◽

Stochastic Volatility Models ◽

Volatility Models

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CLOSED FORM FORMULAS FOR EXOTIC OPTIONS AND THEIR LIFETIME DISTRIBUTION

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024999000030 ◽

1999 ◽

Vol 02 (01) ◽

pp. 17-42 ◽

Cited By ~ 22

Author(s):

RAPHAËL DOUADY

Keyword(s):

Interest Rates ◽

Closed Form ◽

Term Structure ◽

Exit Time ◽

Exotic Options ◽

Barrier Options ◽

Double Barrier ◽

Knock Out ◽

The Mean ◽

Mirror Principle

We first recall the well-known expression of the price of barrier options, and compute double barrier options by the mean of the iterated mirror principle. The formula for double barriers provides an intraday volatility estimator from the information of high-low-close prices. Then we give explicit formulas for the probability distribution function and the expectation of the exit time of single and double barrier options. These formulas allow to price time independent and time dependent rebates. They are also helpful to hedge barrier and double barrier options, when taking into account variations of the term structure of interest rates and of volatility. We also compute the price of rebates of double knock-out options that depend on which barrier is hit first, and of the BOOST, an option which pays the time spent in a corridor. All these formulas are either in closed form or double infinite series which converge like e-α n2.

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