【正文】 mesh(X,Y,C39。y=0:100/20:100。end繪圖程序如下：C=heatord(50,0,5,10,20)。 for j=2:M B(j,1) = C(i+1,j)。% end%B,A%qq = inv(A) * B for i=N:1:1 B(1,1) = X。%B(M+1,1) = 0。 A(j+1,j+2)=c(j)。 for j=1:M1 A(j+1,j)=a(j)。A(1,1)=1。end for j=1:M+1C(N+1,j)=max(X(j1)*detaS,0)。 %Boundary conditions for i=1:N+1C(i,1)=c1。c(j)=1/2*r*j*detat1/2*sigma*sigma*j*j*detat。SMAX=detaS*Mfor j=1:M1a(j)=1/2*r*j*detat1/2*sigma*sigma*j*j*detat。 analogous to Table %Initialize parameters and C X = c1。getch()。j++)printf(s[%d][%d]=%f，c[%d][%d]=%f\n,i,j,s[i][j],i,j,c[i][j])。i++){for(j=0。//求剩下節(jié)點的期權(quán)價c//以下輸出結(jié)果 for(i=0。j=i。i=0。else c[t][j]=0。j=t。j++)s[i][j]=pow(u,ij)*pow(d,j)*s[0][0]。i++)for(j=0。//按公式求qfor(i=1。a=exp(r*bigt/t)。//以下求解 u=exp(k*sqrt(bigt/t))。j=0,1,...,i) scanf(%lf,amp。double s[t+1][t+1],c[t+1][t+1]。k,amp。x,amp。scanf(%d %lf %lf %lf %lf,amp。double x,r,k,u,d,q,bigt,a。printf(現(xiàn)已知t，x，r，k及s[0][0]，求解二叉樹上所有節(jié)點的股價s與期權(quán)c\n\n\n)。j=0,1,...,i)表示二叉樹上各節(jié)點的期權(quán)價。j=0,1,...,i)表示二叉樹上各節(jié)點的股價，\n)。printf(x表示執(zhí)行價，r表示利率\n)。}:includeincludemain(){printf(\n本程序解決這樣一個問題：\n)。 }printf(\n因此在0時刻該期權(quán)的價格為c[0][0]=%f\n,c[0][0])。j=i。i=t。j++)c[i][j]=1/(1+r)*(q*c[i+1][j]+(1q)*c[i+1][j+1])。i)for(j=0。//按公式求qfor(i=t1。else c[t][j]=0。j=t。j++)s[i][j]=pow(u,ij)*pow(d,j)*s[0][0]。i++)for(j=0。//以下求解 for(i=1。j=0,1,...,i) scanf(%f,amp。float s[t+1][t+1],c[t+1][t+1]。u,amp。x,amp。scanf(%d %f %f %f %f,amp。float x,r,u,d,q。printf(現(xiàn)已知t，x，r，u，d以及s[0][0]，求解二叉樹上所有節(jié)點的股價s與期權(quán)c\n\n\n)。j=0,1,...,i)表示二叉樹上各節(jié)點的期權(quán)價。j=0,1,...,i)表示二叉樹上各節(jié)點的股價，\n)。printf(x表示執(zhí)行價，r表示利率，u表示上升比例，d表示下降比例，\n)。38參 考 文 獻[1] Louis Bachelier. Theorie de la Speculation[J]. Ann. Sci. Ecole Norm. Sup, 1900, 17(3): 2186.[2] Black F. and M Scholes. The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 1973, 81(4): 637654[3] Cox J C, S. A. Ross and M Rubinstein. Option Pricing A Simplified Approach[J]. Journal of Financial Economics, 1979, 7(3): 229263[4] 李楚霖, 楊明, 易江. 金融分析及其應(yīng)用[M]. 北京: 首都經(jīng)濟貿(mào)易大學(xué)出版社, 2007. 105173[5] Joseph Stampfli, Victor Goodman著, 蔡明超譯. 金融數(shù)學(xué)[M]. 北京: 機械工業(yè)出版社, 2008. 1108[6] 陳佳, 吳潤衡. 金融數(shù)學(xué)中的歐式期權(quán)定價方法[J]. 北方工業(yè)大學(xué)報, 2004, 19(1): 7478[7] 姜禮尚. 期權(quán)定價的數(shù)學(xué)模型和方法[M]. 第二版. 北京: 高等教育出版社, 2008. 9110[8] 楊建奇, 肖慶憲. 期權(quán)定價的方法和模型綜述[J]. 商業(yè)時代, 2008, 16(2): 6581[9] 嚴蔚敏, 吳偉民編著. 數(shù)據(jù)結(jié)構(gòu)[M]. 北京: 清華大學(xué)出版社, 2006. 75153[10] 譚浩強. C程序設(shè)計[M]. 第三版. 北京: 清華大學(xué)出版社, 2006. 106198[11] 史萬明, 孫新, 吳裕樹. 數(shù)值分析[M]. 第二版. 北京: 北京理工大學(xué)出版社, 2004. 160[12] 陸君安, 尚濤, 謝進等. 偏微分方程的MATLAB解法[M]. 湖北: 武漢大學(xué)出版社, 2001. 3585[13] 姜健飛, 胡良劍, 唐儉. 數(shù)值分析及其MATLAB實驗[M]. 北京: 科學(xué)出版社, 2004. 2098[14] 約翰赫爾. 期權(quán)期貨和其他衍生產(chǎn)品[M]. 第三版. 北京: 華夏出版社, 2004. 123344European Option Pricing Theory and Its Numerical MethodsShi Chao(College of Science, South China Agricultural University Guangzhou 510642,China)Abstract: In the wake of the rapid development of financial market, people are giving more and more attention to Option. So, it is necessary to probe into Option. The former scholar did it. In 1973, Fischer Black and Myron Scholes won the Nobel Prize because of establishing the call option pricing formula. The thesis focuses on the pricing of European Option at the aspects of the pricing model and the numerical putation approach. The writer hopes to reach the conclusion through the discussion of the theoretical knowledge and the analysis of examples. The thesis has six chapters. Chapter one represents the background and significance, the former research results and the structure introduction. Chapter two shows the basic knowledge of Option, Option profit and loss, and Option fixed price boundary. Chapter three discusses the Binomial model. It probes into European Option pricing formula during the different periods of stock price movement from the simplest to more plex. In chapter four, the writer analyzes the BlackScholes model. And the BlackScholes formula () is got by solving the BlackScholes equation. Then the relation between the BlackScholes model and the Binomial model, that is to say, Volatility is studied. In chapter five, the writer solves the question about European option pricing with two numerical methods: Binary Tree Chart and Finite Difference method, which includes containing finite difference, extrapolation finite difference and CrankNicolson finite difference. Both numerical methods demand the option prices of the end to pute the option price of the beginning. The writer analysis some examples using puter language to describe the math knowledge and introduces its application. In chapter five, Some conclusions are drawn from the contents discussed above. The thesis mainly talks about investigation for option pricing and its numerical methods, then gives prominence to its application by examples, but what’s not enough is that the theory has little breakthrough. Key words: European Option Pricing Bi