{
  "id": "1608.03352",
  "version": "v1",
  "published": "2016-08-11T02:54:31.000Z",
  "updated": "2016-08-11T02:54:31.000Z",
  "title": "Some Contributions to Sequential Monte Carlo Methods for Option Pricing",
  "authors": [
    "Deborshee Sen",
    "Ajay Jasra",
    "Yan Zhou"
  ],
  "categories": [
    "stat.CO",
    "q-fin.CP",
    "q-fin.PR"
  ],
  "abstract": "Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general, these expectations cannot be calculated analytically, and one way to approximate these quantities is via the Monte Carlo method; Monte Carlo methods have been used to price options since at least the 1970's. It has been seen in Del Moral, P. \\& Shevchenko, P.V. (2014) `Valuation of barrier options using Sequential Monte Carlo' and Jasra, A. \\& Del Moral, P. (2011) `Sequential Monte Carlo for option pricing' that Sequential Monte Carlo (SMC) methods are a natural tool to apply in this context and can vastly improve over standard Monte Carlo. In this article, in a similar spirit to Del Moral, P. \\& Shevchenko, P.V. (2014) `Valuation of barrier options using sequential Monte Carlo' and Jasra, A. \\& Del Moral, P. (2011) `Sequential Monte Carlo for option pricing' we show that one can achieve significant gains by using SMC methods by constructing a sequence of artificial target densities over time. In particular, we approximate the optimal importance sampling distribution in the SMC algorithm by using a sequence of weighting functions. This is demonstrated on two examples, barrier options and target accrual redemption notes (TARN's). We also provide a proof of unbiasedness of our SMC estimate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-11T02:54:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sequential monte carlo methods",
      "option pricing",
      "del moral",
      "barrier options",
      "target accrual redemption notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}