TY - JOUR
T1 - Pricing Continuously Monitored Barrier Options under the SABR Model
T2 - A Closed-Form Approximation
AU - Yang, Nian
AU - Liu, Yanchu
AU - Cui, Zhenyu
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2017/6
Y1 - 2017/6
N2 - 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.
AB - 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.
KW - Closed-form approximation
KW - Continuously monitored barrier option
KW - SABR model
KW - Stochastic volatility
KW - Survival density
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U2 - 10.3724/SP.J.1383.202006
DO - 10.3724/SP.J.1383.202006
M3 - Article
AN - SCOPUS:85106623281
SN - 2096-2320
VL - 2
SP - 116
EP - 131
JO - Journal of Management Science and Engineering
JF - Journal of Management Science and Engineering
IS - 2
ER -