外文翻譯--期貨期權(quán)定價模型和相關(guān)研究（英文）

1、 1The Structure Models for Futures Options Pricing and Related Researches Feng DAI Dongkai ZHAI Zifu QIN Department of Management Science Zhengzhou Information Engineering University, Henan 450002, China E-mail:fe

2、ngdai@public2.zz.ha.cn; fengdai@126.com Abstract：Based on the structure model of option pricing (Feng DAI, 2005) and the Partial Distribution (Feng DAI, 2001), this paper designs a new kind of expression of futures pric

3、e, presents the structure pricing model for American futures options on underlying non-dividend-paying, and gives three put-call parities between American call and put option on spots, call and put option on futures, a

4、nd spot options and futures options, they are different from put-call parity of European options. We prove analytically that an American call option on futures must be worth more than the corresponding American call op

5、tion on spot and an American put option on futures must be worth less than the corresponding American put option on spot in normal market; and the oppositions in inverted market. The final empirical researches also sup

6、port the conclusions in this paper. Key words：structure pricing, American options on futures, non-dividend-paying, analytic formula, put-call parity 1 Introduction In theoretical studies of international economics and f

7、inance engineering, options pricing is an important problem to which economists pay the exceptional attentions. In the studies of option pricing, there have been many significant results (Black and Scholes 1973, Merton

8、 1976, Sharpe 1978, Whaley 1981, Gesk and Roll 1984), and approximation methods for American put option (MacMillan 1986, Stapleton and Subrahmanyam 1997). “Unfortunately, no exact analytic formula for the value of an A

9、merican put option on a non-dividend-paying stock has been produced” [9]. The authors of this paper have solved the problem in reference [10]. And in this paper, author will present the structure pricing model for Amer

10、ican futures options on underlying non-dividend-paying. In addition, when the futures and options contracts have the same maturity, and “Suppose that there is a normal market with futures prices consistently higher t

11、han spot prices prior to maturity. ….An American call futures option must be worth more than the corresponding American call option on the underlying assets. …. Similarly, An American put futures option must be worth l

12、ess than the corresponding American put option on the underlying assets. If there is an inverted market with futures prices consistently lower than spot prices, …, the reverse must be true. American call futures option

13、s are worth less than the corresponding American call option on the underlying assets, whereas American put futures options are worth more than the corresponding American put option on the underlying assets” [9]. The r

14、eal trade in market shows that the conclusions above are true. But, in this paper, we shall prove them in analytic way, and give computing method for the deference between the values of American futures option and the

15、 corresponding American option on the underlying assets. By the way, this paper will presents three kinds of put-call parity, i.e. put-call parity of call spot option and put spot option, put-call parity of call futures

16、 option and put futures option, and put-call parity of call spot option, put spot option, call futures option and put futures option. The former two of put-call parity here have small differences with those we have kno

17、wn in expression, and the later one is a new. 2 The Basic Assumptions for the Prices of Assets and the Partial distribution 2.1 The basic assumptions of prices of assets The basic assumptions we use to define the pric

18、e of an underlying assets (spot, stock and stock indices), regarded as the basis of the discussion in this paper are as follows: Assumption 1. 1) The prices of an underlying assert includes the cost price and the mar

19、ket price. The cost price means the average value of all the prices paid by the market traders to produce or buy an underlying asset and the 3 general, the futures price is expressed as (see reference [9]): F(t)=S(t)eδt

20、 (1) In (1), S(t) is the underlying asset price. For a non-dividend-paying asset, if it is an investment asset, δ=c, i.e. c=r; if it is a consumption asset, δ=c-y. W

21、here, c is the cost of carry, r is the risk-free rate, y is the convenience yields. In fact, if F(t)=S(t)eδt, thus the distribution function PF{F(t)0, b=0, we define: ba e? = zaz e?→ + 0 lim =0. Definition 4(DF stru

22、cture). Let X be the value of an asset related to an underlying asset A(t)∈P(µ(t), σ2(t)), if ? t∈[0,∞) and T>t, XA(t,T)∈P(X, D[A(t)](T-t)), then we call XA(t,T) the DF stochastic structure of X on A(t). XA(t,T)

23、 is called a DF structure of X for short. Where, A(t) can be the price of an underlying asset or a futures contact. For any t∈[0,∞], if S(t) is the market price of an spot asset, T is the expiration time of derivatives

24、 on S(t), and X is the strike price of the derivatives, thus the DF stochastic structure of strike price X on S(t) is XS(t,T)∈P(X,D[S(t)](T-t)). Similarly, YF(t, T) is the DF stochastic structure of strike price Y on f

25、utures F(t), thus YF(t,T)∈P(Y, D[F(t)](T-t)). Although the futures has certain connections with its DF structure YF(t, T) in changing, their stochastic movements may have no inevitable relation, so we could suppose th