HW8

OIL BOND

𝑏𝑜𝑛𝑑𝑝𝑟𝑖𝑐𝑒={ $1000 ,𝑜𝑖𝑙<25$1000+(𝑜𝑖𝑙−25 )×$170 ,25≤𝑜𝑖𝑙≤40

$3550 ,𝑜𝑖𝑙>40

OIL BOND - CODES = 30;r = 0.02;sigma = 0.06;T = 1;N = 10; deltaT = T/N;u = exp( sigma * sqrt(deltaT) );d = 1/u;p = ( exp( r * deltaT ) - d ) / ( u - d );

for i = 0 : N oilp(i+1) = S * u^(N-i) * d^(i); if oilp(i+1)<25 oilp(i+1) = 25; elseif oilp(i+1)>40 oilp(i+1) = 40; end oilp(i+1) = 1000+( oilp(i+1) -25)*170;end

OIL BOND – CODE (CONTI.)for i = N : -1 : 1 for j = 0 : i-1 oilp(j+1) = exp(-r*deltaT) * ( oilp(j+1)*p + oilp(j+2)*(1-p) ); end oillattice(1:i,i) = oilp(1:i);end format short goilp(1,1)oillattice

INDEX CURRENCY OPTION NOTES

INDEX CURRENCY OPTION NOTES

- CODES = 102;r = 0.02;sigma = 0.102;T = 1;N = 10; deltaT = T/N;u = exp( sigma * sqrt(deltaT) );d = 1/u;p = ( exp( r * deltaT ) - d ) / ( u - d );

for i = 0 : N currp(i+1) = S * u^(N-i) * d^(i); if currp(i+1)>169 currp(i+1) = 1000; elseif currp(i+1)<84.5 currp(i+1) = 0; else currp(i+1) = 1000-(1000*(169/currp(i+1)-1)) ; endend

INDEX CURRENCY OPTION NOTES

- CODE (CONTI.)for i = N : -1 : 1 for j = 0 : i-1 currp(j+1) = exp(-r*deltaT) * ( currp(j+1)*p + currp(j+2)*(1-p) ); end currlattice(1:i,i) = currp(1:i);end format short gcurrp(1,1)currlattice

MONTE CARLO PUT OPTIONfunction [ cp, pp, CIc, CIp] = blsMC( S, K, r, T, sigma, NRepl ) nuT = (r - 0.5*sigma^2) * T;siT = sigma * sqrt(T);c_payoffs = exp(-r*T) * max(0, S*exp(nuT + siT*randn(NRepl,1)) -K );p_payoffs = exp(-r*T) * max(0, K - S*exp(nuT + siT*randn(NRepl,1)) ); [cp, varc, CIc] = normfit(c_payoffs); [pp, varp, CIp] = normfit(p_payoffs);

end

DEMOS = 50; K = 50; r = 0.1; T = 1; sigma = 0.2; lamda = 1.2;

[blsout_c, blsout_p] = blsprice(S,K,r,T,sigma);bls = ones(100) * blsout_p; for i = 1:100 [bitc(i), bitp(i)] = bitprice(S,K,r,T,sigma,i,0); [tric(i), trip(i)] = triprice(S,K,r,T,sigma,lamda,i,0); [MCc(i), MCp(i), temp1,temp2] = blsMC(S,K,r,T,sigma,i*100); CId(i) = temp2(2)-temp2(1);end

CASH OR NOTHINGfunction [ cp, pp ] = blsMC2( S, K, C, r, T, sigma, NRepl )

nuT = (r - 0.5*sigma^2) * T;siT = sigma * sqrt(T);pvC = exp(-r*T) * C;

Stock = S*exp(nuT + siT*randn(NRepl,1));

for i = 1:NRepl c_payoffs(i) = 0; p_payoffs(i) = 0; if Stock(i) > K c_payoffs(i) = pvC; elseif Stock(i) < K p_payoffs(i) = pvC; endend

[cp, varc, CIc] = normfit(c_payoffs); [pp, varp, CIp] = normfit(p_payoffs); end

DEMOS = 50; K = 50; C = 10; r = 0.1; T = 1; sigma = 0.2; NRpel = 10000; for TS = 1:100 [MC1c(TS), MC1p(TS)] = blsMC2(TS,K,C,r,T,sigma,NRpel);End

figure;plot(MC1c);hold on;plot(MC1p,'color',[1 0 0.5]);title('Cash or Nothing');