The valuation of barrier options under a threshold rough Heston model

In this paper,we propose a novel model for pricing double barrier options,where the asset price is modeled as a threshold geometric Brownian motion time changed by an integrated activity rate process,which is driven by the convolution of a fractional kernel with the CIR process.The new model both captures the leverage effect and produces rough paths for the volatility process.The model also nests the threshold diffusion,Heston and rough Heston models.We can derive analytical formulas for the double barrier option prices based on the eigenfunction expansion method.We also implement the model and numerically investigate the sensitivities of option prices with respect to the parameters of the model.

Pricing Continuously Monitored Barrier Options under the SABR Model:A Closed‐Form Approximation

The stochastic alpha beta rho(SABR)model introduced by Hagan et al.(2002)is widely used in both fixed income and the foreign exchange(FX)markets.Continuously monitored barrier option contracts are among the most popular derivative contracts in the FX markets.In this paper,we develop closed-form formulas to approximate various types of barrier option prices(down-and-out/in,up-and-out/in)under the SABR model.We first derive an approximate formula for the survival density.The barrier option price is the one-dimensional integral of its payoff function and the survival density,which can be easily implemented and quickly evaluated.The approximation error of the survival density is also analyzed.To the best of our knowledge,it is the first time that analytical(approximate)formulas for the survival density and the barrier option prices for the SABR model are derived.Numerical experiments demonstrate the validity and efficiency of these formulas.

American Barrier Option Pricing Formulas for Currency Model in Uncertain Environment

Option pricing problem is one of the central issue in the theory of modern finance.Uncertain currency model has been put forward under the foundation of uncertainty theory as a tool to portray the foreign exchange rate in uncertain finance market.This paper uses uncertain differential equation involved by Liu process to dispose of the foreign exchange rate.Then an American barrier option of currency model in uncertain environment is investigated.Most important of all,the authors deduce the formulas to price four types of American barrier options for this currency model in uncertain environment by rigorous derivation.

RBSDEs with optional barriers:monotone approximation

In this short note we consider reflected backward stochastic differential equations(RBSDEs)with a Lipschitz driver and barrier processes that are optional and right lower semicontinuous.In this case,the barrier is represented as a nondecreasing limit of right continuous with left limit(RCLL)barriers.We combine some well-known existence results for RCLL barriers with comparison arguments for the control process to construct solutions.Finally,we highlight the connection of these RBSDEs with standard RCLL BSDEs.