HW8

OIL BOND

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

$3550 ,𝑜𝑖𝑙>40

OIL BOND - CODE

S = 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 g

oilp(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)) ;

end

end

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 g

currp(1,1)

currlattice

MONTE CARLO PUT OPTION

function [ 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

DEMO

S = 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 NOTHING

function [ 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;

end

end

[cp, varc, CIc] = normfit(c_payoffs);

[pp, varp, CIp] = normfit(p_payoffs);

end

DEMO

S = 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');