混合双分数布朗运动下的永久美式回望期权定价

doi:10.6040/j.issn.1671-9352.0.2022.629

Abstract

Abstract:

A pricing model for a perpetual American lookback option with dividends driven by mixed bi-fractional Brownian motion is constructed in this paper. First, the partial differential equations of mixed bi-fractional Brownian motion for perpetual American lookback call and put options are given by the Δ-hedging principle. Then, the established partial differential equations are solved by variable substitution method and characteristic equation method. Finally, numerical experiments are adopted to verify the linear proportional scaling properties of the solution, and the effects of mixed bi-fractional Brownian motion parameters H, K and volatility on the option prices are further discussed.

Key words: mixed bi-fractional Brownian motion, perpetual American lookback option, option pricing

CLC Number:

O211.6

Yaru ZHANG,Li XIA,Dianqiu ZHANG. Perpetual American lookback option pricing under mixed bi-fractional Brownian motion[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 98-107.

Figures/Tables 6

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References 18

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H	K	λ₁	λ₂	z_c	C
0.75	0.70	7.691 8	-0.095 3	0.087 0	7.406 3
0.75	0.75	7.237 1	-0.094 3	0.086 2	7.425 0
0.75	0.80	6.821 3	-0.093 3	0.085 3	7.445 0
0.85	0.60	7.885 7	-0.095 7	0.087 3	7.399 0
0.85	0.70	6.874 6	-0.093 4	0.085 5	7.442 0
0.85	0.80	6.046 0	-0.091 1	0.083 5	7.489 0
0.70	0.75	7.691 8	-0.095 3	0.087 0	7.406 3
0.75	0.75	7.237 1	-0.094 3	0.086 2	7.425 0
0.85	0.75	6.440 3	-0.092 3	0.084 5	7.465 0
0.65	0.85	7.354 3	-0.094 6	0.086 4	7.420 0
0.75	0.85	6.440 3	-0.092 3	0.084 5	7.465 0
0.85	0.85	5.687 2	-0.089 8	0.082 4	7.514 0

σ₁	σ₂	λ₁	λ₂	z_c	C
0.20	0.30	6.821 3	-0.093 3	0.085 3	7.444 6
0.25	0.35	5.143 2	-0.087 6	0.080 6	7.559 1
0.30	0.40	4.099 7	-0.081 8	0.075 6	7.681 6
0.35	0.45	3.407 5	-0.076 0	0.070 6	7.807 0
0.40	0.50	2.924 8	-0.070 4	0.658 0	7.931 2

Perpetual American lookback option pricing under mixed bi-fractional Brownian motion

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