YAN Hai-feng, LIU San-yang. New Method to Option Pricing for the General Black-Scholes Model-An Acturarial Approach[J]. Applied Mathematics and Mechanics, 2003, 24(7): 730-738.
Citation: YAN Hai-feng, LIU San-yang. New Method to Option Pricing for the General Black-Scholes Model-An Acturarial Approach[J]. Applied Mathematics and Mechanics, 2003, 24(7): 730-738.

New Method to Option Pricing for the General Black-Scholes Model-An Acturarial Approach

  • Received Date: 2002-01-16
  • Rev Recd Date: 2003-03-13
  • Publish Date: 2003-07-15
  • Using physical probability measure of price process and the principle of fair premium,the results of Mogens Bladt and Hina Hviid Rydberg are generalized.In two cases of paying intermediate divisends and no intermediate dividends,the Black-Scholes model is generalized to the case where the riskless asset(bond or bank account) earns a time-dependent interest rate and risky asset(stock) has time-dependent the continuously compounding expected rate of return,volatility.In these cases the accurate pricing formula and put-call parity of European option are obtained.The general approach of option pricing is given for the general Black-Scholes of the risk asset(stock) with a stochastic continuously compounding expected rate of return,volatility.The accurate pricing formula and put-call parity of European option on a stock whose price process is driven by general Ornstein-Uhlenback process are given by actuarial approach.
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  • [1]
    Merton R.Optimum consumption and portfolio rules in continuous time model[J].Journal of Economic Theory,1971,3(3):373-413.
    [2]
    Black F,Scholes M.The pricing of options and corporate liabilities[J].Journal of Political Economy,1973,81(4):633-654.
    [3]
    Duffie D.Security Markets:Stochastic Models[M].Boston:Academic Press,1988.
    [4]
    Bladt M,Rydberg H T.An actuarial approach to option pricing under the physical measure and without market assumptions[J].Insurance:Mathematics and Economics,1998,22(1):65-73.
    [5]
    Duffie D.Dynamic Asset Pricing Theory[M].Princeton,New Jersey:Princeton University Press,1996.
    [6]
    Merton R.Continuous-Time Finance[M].Oxford:Blacwell Publishers,1990.
    [7]
    Kouritzin M A,Deli Li.On explicit solution to stochastic differential equation[J].Stochastic Analysis and Applications,2000,18(4):571-580.
    [8]
    薛宏.鞅方法在未定权益定价中的应用[J].工程数学学报,2000,17(1):135-138.
    [9]
    Roos Cox J C,Rubinstein S A.Option pricing:A simplified approach[J].Journal of Economics,1979,7(2):229-263.
    [10]
    Bernt,Фksendal.Stochasitc Differential Equations[M].Fourth Ed.New York:Springer-Verlag,1995.
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