Pricing Options Based on Trinomial Markov Tree

Table 1

Sensitivity of volatilities.

Strike	Market	B-S	Trinomial	𝑎=0.005	𝑎=0.006	𝑎=0.007	𝑎=0.008	𝑎=0.009
40	34.49	36.57	36.39	35.76	35.58	35.43	35.32	35.46
48	27.48	29.85	29.54	28.44	28.30	28.18	28.09	28.21
56	20.9	23.96	23.53	22.07	21.64	21.33	21.10	21.40
60	17.78	21.36	20.86	19.32	18.91	18.61	18.39	18.67
64	15.03	18.99	18.40	16.56	16.17	15.89	15.69	15.94
72	10	14.9	14.29	11.04	10.70	10.44	10.27	10.49
80	6.26	11.6	10.96	7.78	7.42	7.15	6.96	7.20
88	3.7	8.99	8.33	6.22	5.78	5.46	5.24	5.53
120	0.32	3.17	2.72	1.61	1.45	1.33	1.24	1.36
160	0.01	0.87	0.65	0.31	0.28	0.26	0.24	0.27

Note: the first column is the strike price, the second is the market price, and the third is the price calculated by B-S model while the forth is calculated by the trinomial tree. The latter columns are the prices calculated by the proposed model when 𝑎 is the corresponding value.