23
votes
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Delta-Hedging Exotic Options
Consider reading Lorenzo Bergomi's excellent book -- or at least the first chapter available here for download --, it will help you clarify things.
Some remarks as to your original question:
It is ...
- 14.5k
10
votes
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For pricing, what types of Exotic Options are suitable using Local Volatility Model or a Stochastic Volatility Model?
Whenever you use any model to price anything, all you need to do is make sure you model the underlying dynamics that the product you're pricing actually depends on.
Any product will be dependent on ...
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9
votes
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What is the name and payoff of this exotic option (where the holder can lock in a price)?
The option described is called a "Shout" option.
- 5,662
8
votes
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Multithreading Monte-Carlo pricing in QuantLib for a single product
Yes, it can work. However, keep in mind that:
you'll be safer if you don't share any objects between threads; see my answer here, in particular the last point;
even if you use different seeds, there'...
- 6,963
6
votes
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What Positions on an Underlier CANNOT be Hedged with Vanillas?
Any non path dependent European type payoff $f(S_T)$ can be replicated in a model independent way with vanilla calls and puts provided $f$ is twice differentiable (in the distribution sense). This is ...
- 5,622
6
votes
How to price a phoenix and snowball type autocallable options?
Typically structures like this are traded as notes. They will be sold at a face value of 100%, where that is normally the combination of a zcb (ie 1y usd, say 97.5%), expected coupon (say +10%), short ...
- 2,531
6
votes
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Pricing an Option with payoff $\left(1-\frac{K}{S_t}\right)^{+}$
$\frac{1}{S_t}$ is log-normal
If $S_t$ is a geometric Brownian motion, so is $\frac{1}{S_t}$ and indeed any power $S_t^\alpha$. Simply use Itô's Lemma and set $f(t,x)=\frac{1}{x}$,
\begin{align*}
\...
- 15.2k
6
votes
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Requesting for price?
As @noob2 noted, nobody is going to quote you a price unless you're a customer. And when I say "customer", I mean "customer of the desk", not just of the bank. Would require an ...
- 2,209
6
votes
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Pricing of European options on two underlying assets
Your statement of the problem is not very detailed. Are $\mu_{S/X}$ constant ? What about interest rates? In the classic exchange option problem, where the payoff is $(X_T - S_T)^+$, they actually do ...
- 2,570
5
votes
Derivation of the formulas for the values of European asset-or-nothing and cash-or-nothing options
You can derive these formulae by tweaking the black scholes derivation. If you are using PDE method, you will use different boundary conditions. If you are using integration over the risk neutral ...
- 16.6k
5
votes
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How is the Chooser Option's value computed in this example?
Although the answer of @SRKX is right on spot, I was already writing a solution along the lines of how you had specifically approached the problem. I think it might still be useful to you, so here it ...
- 14.5k
5
votes
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Is the asset-or-nothing call option in this example valued incorrectly in the Black-Scholes framework?
I agree with your computations. The problem is that the initial price of the asset-or-nothing call of 38.66 can't arise within the Black-Scholes framework. This seems to be an inconsistency/error in ...
- 5,959
5
votes
Multithreading Monte-Carlo pricing in QuantLib for a single product
Adding to Luigi's answer, second point: The issue of overlapping Mersenne Twister sequences can be addressed with dynamically created Mersenne Twister Generators, cf. http://www.math.sci.hiroshima-u....
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5
votes
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Flaw in the following argument with Binary Options and Skew
Let $f_0(S_T) =f(S_T|S_0)$ be the risk-neutral PDF for the underlying asset price at time $T$ (conditional on the price $S_0$ at present time $t=0$). The probability that the price is above a strike ...
- 3,595
5
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Can we use Black-Scholes to price path dependent options?
It depends very much on the individual option you are pricing.
Sometimes you can get a Black-Scholes PDE with some extended state and boundary conditions.
up-and-out barrier option will have ...
- 427
5
votes
Monte Carlo approximation of call option on the maximum of two assets
I image you want to calculate the following payoff:
$$\pi_T = \max\left[ \max(S_T^1, S_T^2) - K, 0 \right]$$
If dynamics are expressed with the following dynamic (from your code, it should be the case)...
- 382
4
votes
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PDE of barrier and lookback options
The difference is that the barrier option is weakly path dependent while the lookback option is strongly path dependent.
In case of a knock-out barrier option, conditional on the option being alive ...
- 5,959
4
votes
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Pricing for an Odd Type of Asset or Nothing Option
The price is, under the risk-neutral measure, $$ P_t = e^{-r(T-t)}\mathbb E[S_T^1 \mathbb 1(S_T^2\le K)\mid \mathcal F_t].$$ Since the risk-neutral asset processes are independent geometric brownian ...
- 605
4
votes
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Pricing and hedging fund-linked derivatives
For Q1 in order to create a negative delta product you would have to offset it by selling a positive delta product to someone else, which is certainly possible.
Q2 I agree with the proxy solution ,...
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4
votes
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Exotic Trading Basic Questions - Banking
"pricing" am autocallables is simply working out what it's worth. This is done by having some model (Google local vol / stochastic local vol) which is calibrated to the market (ie listed vanilla ...
- 2,531
4
votes
Autocall pricing: what does "Lipschitz continuous parameterization" mean?
It sounds to me that they just mean that each bound can be seen as a function of the parameter(s) in the parametrization and this function is Lipschitz continuous.
An example: Consider the XY-plane. ...
- 661
4
votes
Undergraduate research topic in options
This question will probably get closed soon, but I'll take a stab at answering anyway.
I think, for an undergraduate, an interesting topic would be the FX-credit hybrids, that is, FX options (or even ...
- 11.9k
4
votes
Monte Carlo approximation of call option on the maximum of two assets
I believe something is wrong with your analytical pricing formula:
I have provided an R script for the analytical pricing formula specified on (p. 211) and it gives a call price of 0.2853.
...
- 4,186
3
votes
Increasing the correlation of two asset reduce the value of spread option.
the payoff is max(X-Y-K,0). so this option pays you the most if X goes up and Y goes down. So you need X and Y to move in opposite directions. The more X and Y move in the same direction (high rho) ...
- 1,558
3
votes
Accepted
Pricing of a Forward-start option in a Black-Scholes framework
The proof is fine. For example, $D(t)S(t)$ is a martingale and then
\begin{align*}
E\big(D(t)S(t)\big) = S(0).
\end{align*}
Regarding the function $C(1, T-T_0, K)$, it is the value, at time $T_0$, ...
- 21k
3
votes
Pricing Exotics: Monte-Carlo is too slow?
You're using a wrong tool for the job. Write your Monte Carlo in a faster language (Java would probably suffice, if not than C++ which is standard for such things). Then you will be able to ...
- 3,242
3
votes
Delta-Hedging Exotic Options
Delta-hedging can be seen from banks as "manufacturing the product".
Banks are product manufacturers, so they delta-hedge.
Exotic options are options which are not volatility-only products.
They ...
- 2,412
3
votes
Derivation of the formulas for the values of European asset-or-nothing and cash-or-nothing options
To add a bit to Will Gu's answer:
Compute $\mathbb{E} \left[ \left. S_T \right| S_T > K \right]$ using the fact that $S_T$ is lognormally distributed with mean $ln(S_0) + (r - \sigma^2/2)T$ and ...
- 61
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