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24 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 ...
Quantuple's user avatar
  • 14.7k
11 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 ...
will's user avatar
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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.
AlRacoon's user avatar
  • 6,612
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'...
Luigi Ballabio's user avatar
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 ...
Antoine Conze's user avatar
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 ...
will's user avatar
  • 2,571
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*} \...
Kevin's user avatar
  • 16k
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 ...
user42108's user avatar
  • 2,262
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 ...
siou0107's user avatar
  • 2,680
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 ...
dm63's user avatar
  • 17.2k
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 ...
Quantuple's user avatar
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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 ...
LocalVolatility's user avatar
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....
Peter Caspers's user avatar
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 ...
RRL's user avatar
  • 3,680
5 votes

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 ...
starovoitovs's user avatar
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)...
Yoda And Friends's user avatar
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 ...
LocalVolatility's user avatar
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 ...
spaceisdarkgreen's user avatar
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 ,...
dm63's user avatar
  • 17.2k
4 votes
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How frequently is local volatility calibrated to implied vol surface, in practice?

I worked on a single name Equity Derivatives trading desk. Implied volatility is remarked at least once per day, but that depends also on market movements, volatility movements, volumes, etc. For this ...
Vitomir's user avatar
  • 821
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 ...
will's user avatar
  • 2,571
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. ...
Jesper Tidblom's user avatar
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 ...
Dimitri Vulis's user avatar
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. ...
Pleb's user avatar
  • 4,286
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) ...
mbison's user avatar
  • 1,578
3 votes
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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 $T_0$, ...
Gordon's user avatar
  • 21.1k
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 ...
quant_dev's user avatar
  • 3,252
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 ...
M. Jeunesse's user avatar
  • 2,422

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