Calculate the price at time t=0Convexity of BS Equation for Call and Putprice of a “Cash-or-nothing binary call option”How to prove price of Asian option under geometric averaging is cheaper than a European call?Time-zero price of two specific contingent claimsWhy $N(d_1)$ and $N(d_2)$ are different in Black & ScholesExpected option return in MATLABBlack-Scholes call option formula, which probability measureCalculate volatility under the binomial model for option pricingAttempt of an analytical proof that a call price decreases as its strike increasesBlack-Scholes European call price taking limits
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Calculate the price at time t=0
Convexity of BS Equation for Call and Putprice of a “Cash-or-nothing binary call option”How to prove price of Asian option under geometric averaging is cheaper than a European call?Time-zero price of two specific contingent claimsWhy $N(d_1)$ and $N(d_2)$ are different in Black & ScholesExpected option return in MATLABBlack-Scholes call option formula, which probability measureCalculate volatility under the binomial model for option pricingAttempt of an analytical proof that a call price decreases as its strike increasesBlack-Scholes European call price taking limits
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Assume the risk-free bond Bt and the stock St follow the dynamics of the Black & Scholes model
(with interest rate r, stock drift $mu$ and volatility $sigma$).
Calculate the price at time $t = 0$ of a derivative with maturity T and payoff $(S^3_t-K)^+$. I know I need to use the Black Scholes formula for price of a call to find the price of the derivative but the formula also contains $N(d_1)$ and $N(d_2)$ so how would this get affected?
black-scholes finance call
asked 10 hours ago
AnonAnon
262 bronze badges
$endgroup$
add a comment
|
$begingroup$
Assume the risk-free bond Bt and the stock St follow the dynamics of the Black & Scholes model
(with interest rate r, stock drift $mu$ and volatility $sigma$).
Calculate the price at time $t = 0$ of a derivative with maturity T and payoff $(S^3_t-K)^+$. I know I need to use the Black Scholes formula for price of a call to find the price of the derivative but the formula also contains $N(d_1)$ and $N(d_2)$ so how would this get affected?
black-scholes finance call
asked 10 hours ago
AnonAnon
262 bronze badges
$endgroup$
$begingroup$
I don't get the question. Which process is defined by $e^beta tS_t^3$?
$endgroup$
– Sanjay
10 hours ago
add a comment
|
$begingroup$
Assume the risk-free bond Bt and the stock St follow the dynamics of the Black & Scholes model
(with interest rate r, stock drift $mu$ and volatility $sigma$).
Calculate the price at time $t = 0$ of a derivative with maturity T and payoff $(S^3_t-K)^+$. I know I need to use the Black Scholes formula for price of a call to find the price of the derivative but the formula also contains $N(d_1)$ and $N(d_2)$ so how would this get affected?
black-scholes finance call
asked 10 hours ago
AnonAnon
262 bronze badges
$endgroup$
Assume the risk-free bond Bt and the stock St follow the dynamics of the Black & Scholes model
(with interest rate r, stock drift $mu$ and volatility $sigma$).
Calculate the price at time $t = 0$ of a derivative with maturity T and payoff $(S^3_t-K)^+$. I know I need to use the Black Scholes formula for price of a call to find the price of the derivative but the formula also contains $N(d_1)$ and $N(d_2)$ so how would this get affected?
black-scholes finance call
black-scholes finance call
asked 10 hours ago
AnonAnon
262 bronze badges
asked 10 hours ago
AnonAnon
262 bronze badges
edited 4 hours ago
Anon
asked 10 hours ago
AnonAnon
262 bronze badges
asked 10 hours ago
AnonAnon
262 bronze badges
asked 10 hours ago
AnonAnon
262 bronze badges
262 bronze badges
$begingroup$
I don't get the question. Which process is defined by $e^beta tS_t^3$?
$endgroup$
– Sanjay
10 hours ago
add a comment
|
$begingroup$
I don't get the question. Which process is defined by $e^beta tS_t^3$?
$endgroup$
– Sanjay
10 hours ago
$begingroup$
I don't get the question. Which process is defined by $e^beta tS_t^3$?
$endgroup$
– Sanjay
10 hours ago
$begingroup$
I don't get the question. Which process is defined by $e^beta tS_t^3$?
$endgroup$
– Sanjay
10 hours ago
add a comment
|
1 Answer
1
active
oldest
votes
$begingroup$
I don't understand the question but I can try. I think the problem is to find the price of a contingent claim that has payoff $(S_T^3 - K)^+$. The well-known pricing formula is:
beginequation
pi(t)=mathbbE^mathbbQ[e^-r(T-t)(S_T^3 - K)^+|mathcalF_t]
endequation
Now put $Y=S^3$, by using Ito's Lemma
beginequation
dY(t)=dS^3(t)=3S^2(t)dS(t) + frac126S(t)sigma^2S^2(t)dt
endequation
In Black-Scholes model
beginequation
dS(t)=mu S(t) dt + sigma S(t) dW(t)
endequation
So we have:
beginequation
dY(t)=3mu S^3dt + 3sigma^2S^3dt + 3sigma S^3dW=(3mu + 3sigma^2)Ydt + 3sigma YdW
endequation
Now we define
beginalign
tildemu&=3mu + 3sigma^2 \
tildesigma&=3sigma
endalign
Now suppose $Y$ is a new stock with drift $tildemu$ and volatility $tildesigma$ and just substitute in the Black-Scholes formula for an european option with underlying $Y$ and strike $K$.
answered 4 hours ago
ab94ab94
1361 silver badge7 bronze badges
$endgroup$
$begingroup$
Hi sorry, I edited the quesiton now.@ab94
$endgroup$
– Anon
4 hours ago
add a comment
|
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1 Answer
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1 Answer
1
active
oldest
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active
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active
oldest
votes
$begingroup$
I don't understand the question but I can try. I think the problem is to find the price of a contingent claim that has payoff $(S_T^3 - K)^+$. The well-known pricing formula is:
beginequation
pi(t)=mathbbE^mathbbQ[e^-r(T-t)(S_T^3 - K)^+|mathcalF_t]
endequation
Now put $Y=S^3$, by using Ito's Lemma
beginequation
dY(t)=dS^3(t)=3S^2(t)dS(t) + frac126S(t)sigma^2S^2(t)dt
endequation
In Black-Scholes model
beginequation
dS(t)=mu S(t) dt + sigma S(t) dW(t)
endequation
So we have:
beginequation
dY(t)=3mu S^3dt + 3sigma^2S^3dt + 3sigma S^3dW=(3mu + 3sigma^2)Ydt + 3sigma YdW
endequation
Now we define
beginalign
tildemu&=3mu + 3sigma^2 \
tildesigma&=3sigma
endalign
Now suppose $Y$ is a new stock with drift $tildemu$ and volatility $tildesigma$ and just substitute in the Black-Scholes formula for an european option with underlying $Y$ and strike $K$.
answered 4 hours ago
ab94ab94
1361 silver badge7 bronze badges
$endgroup$
$begingroup$
Hi sorry, I edited the quesiton now.@ab94
$endgroup$
– Anon
4 hours ago
add a comment
|
$begingroup$
I don't understand the question but I can try. I think the problem is to find the price of a contingent claim that has payoff $(S_T^3 - K)^+$. The well-known pricing formula is:
beginequation
pi(t)=mathbbE^mathbbQ[e^-r(T-t)(S_T^3 - K)^+|mathcalF_t]
endequation
Now put $Y=S^3$, by using Ito's Lemma
beginequation
dY(t)=dS^3(t)=3S^2(t)dS(t) + frac126S(t)sigma^2S^2(t)dt
endequation
In Black-Scholes model
beginequation
dS(t)=mu S(t) dt + sigma S(t) dW(t)
endequation
So we have:
beginequation
dY(t)=3mu S^3dt + 3sigma^2S^3dt + 3sigma S^3dW=(3mu + 3sigma^2)Ydt + 3sigma YdW
endequation
Now we define
beginalign
tildemu&=3mu + 3sigma^2 \
tildesigma&=3sigma
endalign
Now suppose $Y$ is a new stock with drift $tildemu$ and volatility $tildesigma$ and just substitute in the Black-Scholes formula for an european option with underlying $Y$ and strike $K$.
answered 4 hours ago
ab94ab94
1361 silver badge7 bronze badges
$endgroup$
$begingroup$
Hi sorry, I edited the quesiton now.@ab94
$endgroup$
– Anon
4 hours ago
add a comment
|
$begingroup$
I don't understand the question but I can try. I think the problem is to find the price of a contingent claim that has payoff $(S_T^3 - K)^+$. The well-known pricing formula is:
beginequation
pi(t)=mathbbE^mathbbQ[e^-r(T-t)(S_T^3 - K)^+|mathcalF_t]
endequation
Now put $Y=S^3$, by using Ito's Lemma
beginequation
dY(t)=dS^3(t)=3S^2(t)dS(t) + frac126S(t)sigma^2S^2(t)dt
endequation
In Black-Scholes model
beginequation
dS(t)=mu S(t) dt + sigma S(t) dW(t)
endequation
So we have:
beginequation
dY(t)=3mu S^3dt + 3sigma^2S^3dt + 3sigma S^3dW=(3mu + 3sigma^2)Ydt + 3sigma YdW
endequation
Now we define
beginalign
tildemu&=3mu + 3sigma^2 \
tildesigma&=3sigma
endalign
Now suppose $Y$ is a new stock with drift $tildemu$ and volatility $tildesigma$ and just substitute in the Black-Scholes formula for an european option with underlying $Y$ and strike $K$.
answered 4 hours ago
ab94ab94
1361 silver badge7 bronze badges
$endgroup$
I don't understand the question but I can try. I think the problem is to find the price of a contingent claim that has payoff $(S_T^3 - K)^+$. The well-known pricing formula is:
beginequation
pi(t)=mathbbE^mathbbQ[e^-r(T-t)(S_T^3 - K)^+|mathcalF_t]
endequation
Now put $Y=S^3$, by using Ito's Lemma
beginequation
dY(t)=dS^3(t)=3S^2(t)dS(t) + frac126S(t)sigma^2S^2(t)dt
endequation
In Black-Scholes model
beginequation
dS(t)=mu S(t) dt + sigma S(t) dW(t)
endequation
So we have:
beginequation
dY(t)=3mu S^3dt + 3sigma^2S^3dt + 3sigma S^3dW=(3mu + 3sigma^2)Ydt + 3sigma YdW
endequation
Now we define
beginalign
tildemu&=3mu + 3sigma^2 \
tildesigma&=3sigma
endalign
Now suppose $Y$ is a new stock with drift $tildemu$ and volatility $tildesigma$ and just substitute in the Black-Scholes formula for an european option with underlying $Y$ and strike $K$.
answered 4 hours ago
ab94ab94
1361 silver badge7 bronze badges
answered 4 hours ago
ab94ab94
1361 silver badge7 bronze badges
answered 4 hours ago
ab94ab94
1361 silver badge7 bronze badges
answered 4 hours ago
ab94ab94
1361 silver badge7 bronze badges
1361 silver badge7 bronze badges
$begingroup$
Hi sorry, I edited the quesiton now.@ab94
$endgroup$
– Anon
4 hours ago
add a comment
|
$begingroup$
Hi sorry, I edited the quesiton now.@ab94
$endgroup$
– Anon
4 hours ago
$begingroup$
Hi sorry, I edited the quesiton now.@ab94
$endgroup$
– Anon
4 hours ago
$begingroup$
Hi sorry, I edited the quesiton now.@ab94
$endgroup$
– Anon
4 hours ago
add a comment
|
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$begingroup$
I don't get the question. Which process is defined by $e^beta tS_t^3$?
$endgroup$
– Sanjay
10 hours ago