# Tag Info

5

$\frac{1}{S_t}$ 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*} \mathrm{d}f(t,S_t) &= \left(0-\mu S_t\frac{1}{S_t^2}+\frac{1}{2}\sigma^2S_t^2\frac{2}{S_t^3}\right)\mathrm{d}t-\sigma S_t \frac{1}{S_t^2}\mathrm{d}W_t \\ &=-...

5

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): $$dS_t^i = rS_t^idt + \sigma S_t^idW_t^i$$ where $W = (W^1, W^2)$ is two dimensional SBM, then, I guess you could simplify your code a bit! From your ...

4

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. library(pbivnorm) maxassets_analytical <- function(r, T, K, sigma1, sigma2, S1, S2, b1, b2, rho){ y1 <- (log(S1/K) + (b1 + sigma1^2/2)*T)/ (sigma1*sqrt(T)) y2 ...

4

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 linear products like FX forwards and xccy swaps) with kick-in or kick-out on a credit event. For example - I want (the right) to exchange USD into EUR at some ...

4

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. Let $Y(x)$ be a function of $x$. This function can be seen as describing the upper bound of the area below the graph. This function can then have the Lipschitz ...

3

That looks correct, but a bit complicated. We know that under Black-Scholes with no dividends, $E^Q(S_t) = Forward = S_0 e^{rt}$ $e^{-rT}E^Q(\int_0^TS_tdt) = e^{-rT}\int_0^TE^Q(S_t)dt \\ = e^{-rT}\int_0^T S_0 e^{rt} dt = S_0 e^{-rT}\int_0^T e^{rt} dt \\ = S_0 e^{-rT} \frac{1}{r}(e^{rT} - 1) = S_0\frac{1-e^{-rT}}{r}$ It is straightforward to generalize to the ...

3

This is not an answer but a comment which is way too long for the comments section. What you can trade will be very much restricted by where you live. In Europe, you have Priips, which changes the game a lot - even US-ETFs are generally not easily available on most platforms (within Europe). How much money do we actually talk about?. No need to answer this ...

2

Some retail investors can get exposure to many exoitic payoffs via bespoke structured notes. Take a look, for example, at https://haloinvesting.com/platform/ and https://www.simon.io/ . You don't need an ISDA agreement to buy a structured note.

2

Exotic Options and Hybrids: A Guide to Structuring, Pricing and Trading, Wiley, 2010. https://www.amazon.co.uk/dp/B003F8S7B8/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1 was quite interesting, and I think you can probably find it on the web somewhere.

1

Generally, FINCAD is correct. I do have some reservations though. Yes, variance swaps have a theoretical replication. A vanilla option trader following a delta-hedging strategy is essentially replicating the payoff of a weighted variance swap where the daily squared returns are weighted by the option’s dollar gamma. Taking this argument one step further, a ...

1

For "Classic Autocall" or "Athena", the coupons are indeed accumulated and paid on the event of autocall, either pre-maturity or at maturity (but for the later it will not be called autocall). So only one barrier level (without considering the down-and-in put), the one of the autocall, or we could say the autocall barrier and coupon ...

1

"Applied Quantitative Finance for Equity Derivatives" by Jherek Healy might be of interest to you though it's not focused specifically on exotics. The sellside (especially French banks) should have primers on exotics though given they're effectively sales pitches, they might not have the detail you're looking for.

1

Since other answers already mentioned Das vol 1 and vol 2 ; and Bouzoubaa and Osseiran, I would like to add the good old: Harry Kat. Structured Equity Derivatives: The Definitive Guide to Exotic Options and Structured Notes. Wiley (2001) (not a very deep discussion of pricing, but good explanation of the product). Marcus Overhaus, Ana Bermudez, Hans ...

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Satyajit Das Structured Products Volume 1: Exotic Options; Interest Rates and Currency (The Das Swaps and Financial Derivatives Library) to volume 3

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