# Tag Info

8

The payoff $\max\{a\cdot S_t - K,0\}$ can be re-written as $a\cdot\max\{S_t - K/a,0\}$. Therefore it can be priced as a regular call option with the strike $K/a$.

4

Liquidity Since this is an asset class which is so tightly coupled with interest rates - it makes good products for clients inherently complex. It also makes good sense to make wider markets for more exotic products than the plain vanilla ones - in which razor-thin spreads rule (and trading huge notionals is not everyone's cup of tea)

3

Sigh. I'm not sure that there's a best way to do multi-threaded MC in QuantLib. I'm afraid that you're underestimating the amount of development you'd need for option 2. You're not going to get away with some OpenMP code as you suggest, because calculations on different paths are not trivially parallel: the RNGs we have are not parallel, and even if you ...

3

I don't know if these are the most commonly traded or most popular (for your definition of popular) but here are a few exotic products that I recall being supported by the flagship product at my former employers. Exotic Options: Asian - Strike price is dependant on average price throughout the deal, not just at expiry Bermudan - So called because it's ...

2

I know this may sound extreme, but in my experience for these kind of payoffs you do need a LMM and possibly with at least 8 factors. There is no shortcut unfortunately, even a 3 factor gaussian model, which you can use to price faster using trees, will not capture the possible dynamics of the curve implicit in an 8 factor LMM. Just my modest opinion ...

2

It is possible to price CRAs using the LMM using a Brownian bridge technique. You simulate to each coupon date and then infer the expectation of the coupon given the values of the rates at the start and end of the accrual period. http://ssrn.com/abstract=1461285 Interpolation Schemes in the Displaced-Diffusion LIBOR Market Model and the Efficient Pricing ...

2

As I understand it, the currency derivatives are meant for customers to hedge actual exposure. A foreign distributor obviously has exchange-rate risk, but it's hard to say who actually has risk exposure to the S&P 500. (There's the effect of beta, of course, but it's pretty rare for someone to have tangible---not just CAPM---exposure to the S&P. ...

2

From Wilmott: Trade capture is the process of booking (or capturing) the trade into the systems used within a financial organisation. This may sometimes have to happen multiple times depending on the complexity of the trades and the ability of the systems to be able to capture the economic, non-economic and static details surrounding the deal. ...

2

Some more concrete sources on Barrier option in the B&S setting and PDEs PDE methods for pricing barrier options (quite technical) Pricing Europ ean Barrier Options More of a general remark to PDE approaches in finance Ilya as far as I know the literature on that topic is quite limited. Solving a PDE means solving a PDE - it does not matter in ...

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Here is to continue the above answer of Emcor to make it more explicit. Note that the fact given in the question should instead be \begin{align*} P(\inf \big\{t \in [0, T], B_t +ct = a \big\} \geq T) = 1- \Phi\Big(\frac{a-cT}{\sqrt{T}}\Big) + e^{2ac}\Phi\Big(\frac{-a-cT}{\sqrt{T}}\Big). \end{align*} Then, for $0<t_0\leq T$, \begin{align*} P(\tau \leq ...

2

The claim payoff you describe, $g(M)$, looks to me like a tight butterfly spread that pays off only in one state of the world. Can't you just replicate that by short two calls with strike $K_0$ and long two calls, with strikes one either side at $K_0\pm 1$? Then the price of your option would be $C(K_0+1)+C(K_0-1)-2\cdot C(K_0)$. This is effectively the ...

2

In short answer, Yes: the backward PDE solution with $v(t,L)=0$ and the expectation coincides under the Black-Scholes market. In the one dimensional case, this topic is mathematically treated in the theory of the scale function and the spead measure. See Revez-Yor 3rd.ed. Ch.VII.3 for details. I don't know whether there are some rigorous theories on the ...

1

the call version pays $$I_{S_T > K } S_T$$ the put version pays $$-I_{S_T < K } S_T$$ Subtract to get a pay-off $$S_T.$$ (ignoring the probability zero event of $S_T=K.$) So the prices subtract to give $S_0.$

1

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You can use: Antithetic variates and; Control variates. Both are variance reduction techniques which will allow you to use fewer paths/simulations. Usually antithetic variates are very efficient on their own. Combining both can be a bit tricky. You could start by simulating the value of a plain vanilla call. Then include antithetic variates and/or ...

1

$S_t$ is already under $Q$ (riskfree drift), so you not need to change the measure here. Note that $c:=\left(\frac{r}{\sigma}-\frac{1}{2}\sigma\right)$ and $E\left(1_A\right)=P(A)$. So one computes the European option price as the discounted payoff expectation: $$C=e^{-rT}E\left(1_{\tau\leq T}\right)=e^{-rT}P(\tau\leq T).$$ The option price equals the ...

1

Some techniques I can think of include Use a brownian bridge to get a crossing probability for points near the boundary Use implicit stepping in your PDE solver (which increases smoothness) as opposed to explicit stepping (which "rings" near discontinuities) Employ control variates, by using the same grid to price related instruments having easy analytic ...

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If I am not mistaken, the Feynman-Kac formula is related to the Kolmogorov's backward equation, so I would expect it to be available only for Markov processes. Diffusions are usually of Markovian type, in contrast to general Ito processes or more to say, general semimartinagales. Intuitively, the PDE/PIDE/... will describe the dynamics of ...

1

The easiest way is to use single-expiry volatility that you would get from your volatility surface. It is usually good enough for government work (e.g. to get a sense if you are getting raped by a dealer or to understand your vega risk). A better way is to use local volatility model and the whole volatility surface up to the date of expiry. There is also a ...

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Of your list, usd callable swaps are definitely most popular, as, they are needed by banks to hedge fixed rate mortgages. Ps, jeebs answer is not relevent for the interest rates markets

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Posting this question to a LinkedIn discussion group solicited the following additional answers: The underlying is relatively well understood and simple in a pricing sense. This allows you to put a complex (exotic) payoff on top. The vast majority of FX spot volumes are spread among a small group of G-7 currencies, unlike equities or other markets where ...

1

I've priced similar animals with a naive N-factor method, adding a convexity adjustment for the swap rates. But I'm not sure this is very orthodox...

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