Codes for "Option Pricing and Hedging for Discrete Time Autoregressive Hidden Markov Model"

https://arxiv.org/abs/1707.02019

Modeling Asset Returns

the following models are available for modelisation

• HMM (hidden markov model)
• ARHMM (autoregressive hidden markov model)
• VHMM (multidimentional hidden hidden markov model)
• VARHMM (multidimentional autoregressive hidden hidden markov model)

Est<model>.m for calibrating the models
Gof<model>.m for Goodness-of-fit test
Sim<model>.m for simulation

to simulate some processes, calibrate the different models and run Godness-of-fit test, run:

simulate_and_calibrate.m

Optimal Hedging

the following models are available for hedging:

• Delta-Hedging
  (HedgingError_DH.m)
• Optimal Hedging with Gaussian Returns
  (HedgingError_Gaussian.m OR HedgingGaussian.m + Hedging_Error_Gaussian_ac.m
• Optimal Hedging with HMM Returns and Semi-exact approximation
  (HedgingError_HMM.m OR HedgingHMM.m + Hedging_Error_HMM_ac.m
• Optimal Hedging with HMM Returns and Monte Carlo approximation
  (HedgingError_HMM_MC.m OR HedgingHMM.m + Hedging_Error_HMM_ac.m
• Optimal Hedging with ARHMM Returns and Semi-exact approximation
  (HedgingError_ARHMM.m OR HedgingARHMM.m + Hedging_Error_ARHMM_ac.m
• Optimal Hedging with ARHMM Returns and Monte Carlo approximation
  (HedgingError_ARHMM_MC.m OR HedgingARHMM.m + Hedging_Error_ARHMM_ac.m

to price an option and hedge it under multiple simulations, run:

simulate_and_hedge.m

this script will reproduce Figure 8: