Questions tagged [exotics]

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Single barrier options in stochastic volatility models

In this note/sketch, I derive among others a closed-form formula for an up and in put (UIP) in stochastic volatility models of the form $$ dS(t) = \sigma(t) S(t) \left[ \rho dW(t) + \sqrt{1-\rho^2} dZ ...
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How does the issuer of a Barrier Reverse Convertible determine the coupon?

I am looking into BRC's, and I keep reading about their relatively high coupon rates which are pre-determined by the issuer. However, I can't seem to find any good resources on HOW they pre-determine ...
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1 vote
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Basic Autocall question

I'm pretty new in structured products area and I have some basics questions regarding autocall : Why the autocall has an automatic redemption feature ? I mean an Investor could be interested in ...
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1 vote
1 answer
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What is the name and payoff of this exotic option (where the holder can lock in a price)?

An exotic option is described as follows: Let $S_t$ be the underlying at $t$. The holder has the option to lock in the current price during the lifetime of the option, which he does for $S_{t}=50$. ...
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Ensuring terminal correlation matches the input correlation on a calendar spread option with unequal fixing dates (Asian arithmetic averaging) MC

This is a rather unique question, which really has no "solution" in the literature that I've run across. We have a Monte Carlo simulation that simulates all the "fixing dates" of ...
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1 answer
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Pricing of European options on two underlying assets

Is anybody able to give the solution to the following problem? Suppose we have two assets, each of which follows a GBM process, and where $dW_S$ and $dW_X$ are correlated $(dW_SdW_X=\rho)$. $dS=\mu_s ...
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2 answers
201 views

Requesting for price?

Just for education purpose. Assuming I have some trading ideas that involves the use of OTC derivatives but I may not be able to put them into practice due to regulatory issues and huge minimum ...
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0 answers
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Is there an analogous strikeFromDelta implementation for 1st gen barrier options?

I have a simple replication pricing implementation for 1st gen exotics (digitals, single and double barriers, etc.). In order to effectively test strategies I want to price "like" strikes ...
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Can I combine the exotics for a payout?

Can I combine a one touch option(barrier lower than current price) and no touch option(barrier higher than current price), so that I get a payout immediately only if the one touch barrier is breached ...
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Exotics - Combination of different payoffs using Black-Scholes

I'm currently struggling with the derivation of a formula to price the following exotic option with Black-Scholes. The option has the maximum payoff of $(S_T-z)$ and $(y - S_T)$, where $S_T$ is the ...
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Structuring and Customization

It seems complex derivatives in particular exotic options are not available at any retail broker. Can a regular retail trader get access to these instruments? Maybe through prop firms or banks? ...
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2 answers
217 views

Monte Carlo approximation of call option on the maximum of two assets

I want to compute the price of the option with payoff \begin{equation} \max \big\{\max\{S^1_T, S^2_T\} - K, 0\big\}, \end{equation} where $S^{1,2}$ have the same dynamics with 0 correlation. So, \...
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Discrete geometric asian option, analytic vs MC

I am attempting to price a discrete geometric Asian option using both the closed form formula (can be found in section 3.2.2 of 'Monte Carlo methods in Financial Engineering' by Glasserman) and an MC ...
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1 answer
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Floating lookback put, MC vs analytic

I am attempting to price a floating lookback put using the analytic formula. (eg. can be found in Shreve's vol II stochastic calculus section 7.4 or on Wikipedia) and wish to confirm the result by ...
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1 answer
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Valuing Conditional "All Or Nothing" Multi Asset Options

I would like some insight as to how to value modified rainbow options on multiple assets: For example: A multi asset option, Call GOOG with $S_t$ \$1600 that you may exercise if and only if you also ...
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1 answer
216 views

Barrier Reverse Convertible

I am a finance student and during my free time I try to understand more financial products. Today I have found a term sheet for a specific type of barrier reverse convertible but I couldn't understand ...
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Machine/Deep Learning for Exotic Option Pricing - Reference Request

Exotic options, in general, have very time-consuming valuation models. I believe in recent years there has been some research done on using supervised machine/deep learning to predict the valuation ...
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1 answer
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Black Scholes price of exotic claim

Given a time horizon N, I want to know the time-$t$ Black-Scholes fair price of $$\int_0^T S_u du$$ where $S_u$ denotes the time-$u$ stock price. I have used the formula I have been given as follows: $...
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Option where option writer determines type of option to give to holder

I am currently looking at an exotic option that allows the holder, at some time $\tau$, to receive either a call or put — the choice of which is decided by the option writer — of which both have the ...
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1 vote
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using moment matching to price spread options (multi asset)

this is my very first question in this forum, after having been a greed follower since a few years, feeling that I need your help in a topic. I need to price a multi asset option that has the ...
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3 votes
1 answer
330 views

Pricing an Option with payoff $\left(1-\frac{K}{S_t}\right)^{+}$

Let $S_t=S_0 \exp\left\{rt+0.5\sigma^2t+\sigma W_t\right\}$ be the usual GBM model for a Stock price under the money-market numeraire. Suppose we want to price an option with payoff at maturity: $C_T=(...
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2 votes
1 answer
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Valuation of Corridor Variance Swaps

Given that the payout of the Corridor Variance Swap (CVS) is $V \left(\frac{\sum_{n=0}^{N}I}{T_2 - T_0} (\sigma^2 - K^2) \right)$, where $\sigma^2$ is the realized variance within the pre-specified ...
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1 answer
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What's the difference between a normal Autocall and a Phoenix Autocall?

I understand the structure of the autocall, how they're priced and their contingent coupons. What I'm not completely clear on is the difference between a "vanilla" Autocall and a Phoenix ...
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1 answer
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Undergraduate research topic in options [closed]

I'm an undergraduate student in finance with a pretty solid knowledge of financial mathematics and I'm currently picking a topic for my research paper this year. I have already decided I will pick ...
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2 votes
2 answers
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Autocall pricing: what does "Lipschitz continuous parameterization" mean?

I've been reading through this research paper (A Monte Carlo Pricing Algorithm For Autocallables That Allows for Stable Differentiation by T. Alm, B. Harrach, D. Harrach, M. Keller) about a method for ...
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1 vote
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What book(s) would you recommend for structuring and pricing Exotic Products?

I've been looking for good books on structuring equity derivatives (Principal Protected Notes, Autocalls, Lookbacks, Reverse Convertibles etc). I only found ones that discuss mainly the theoretical ...
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2 votes
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Determination of critical stock price in compound option pricing

Under the Black-Scholes framework, there is a closed form formula for the price of a compound options, as first derived by Geske (1979). However, the analytical formula refers to a critical stock ...
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7 votes
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410 views

Autocallable option Delta

There have been numerous exotic trading desk blow ups lately, related to various reasons. However, in particular, one bank had some issues where they were pricing autocallable notes with Local ...
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320 views

COS method option pricing

is the cos method used to calculate prices of options other than the European call? Or is this method only used for calibration? Is it possible to evaluate the barrier and lookback options? I am ...
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Hedge robustness of the one factor Hull White model

I recently came across a quote in a book: "All single factor models share the limitation that shifts in curve levels cause shifts in the package of vanilla options that are a good hedge for the ...
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2 votes
1 answer
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Confusion about optimal choices with exotic options

With exotic options, holders usually face choices at certain times. In my understanding, the price of the option is determined by assuming the optimal choice is taken and computing the discounted ...
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2 votes
0 answers
51 views

Confusion about American style option

In American style exotic options, the holder is often faced with choices at certain times during the life span of the option. Following the/an optimal choice allows the user to maximize the value of ...
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1 vote
3 answers
220 views

Graph of a down-and-in barrier option

Here is a graph of Price vs Spot from Joshi's Quant Interviews book, The first line is a down-and-out barrier option and the other one is a down-and-in barrier option. The strike is 100 and the ...
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1 vote
0 answers
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How to price a down-and-out leveraged barrier call option using Brownian motion?

I am trying to price a type of leveraged down-and-out (LDAO) barrier call option, using geometric Brownian motion. My python script is below. I am not sure how to correctly model the increasing ...
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2 votes
1 answer
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What are the formulas to compute the greeks of a gap option?

I'm having a problem to calculate the gap option greeks since there are 2 different exercise prices K1 and K2. Do you know the answer or where can I read about these particular greeks?
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2 votes
1 answer
272 views

What kind of entities use exotic derivatives, and do they serve any purpose other than hedging risk?

I work in a sell-side bank in derivatives modeling. My work involves modeling and pricing of exotic derivatives and I often wonder who are the buyers of these products. From my research, I found that ...
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3 votes
0 answers
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Pricing/Hedging a yield curve spread option (YCS)

I have 2 perspectives as to what model to use for a YCS option: It is an at the expiry option, so hit the marginals, correlate them with a copula, and be done with it. To hedge the vega, I will need ...
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  • 1,662
2 votes
1 answer
230 views

Bermudan option exercise probability when rates rise

I am looking for an explanation of what happens to the Bermudan exercise probability (i.e. does probability of early exercise go higher if rates rise or lower) w.r.t rates. This is of course with ...
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  • 1,662
2 votes
0 answers
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Local v/s global calibration for a Bermudan Option (calibrate co-terminals vs entire matrix)

I am quite new to rates modeling and I have a question on the pros and cons of calibrating to larger set of vanilla instruments v/s calibrating to an exotic's 'natural' hedges. For example, I could ...
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  • 1,662
0 votes
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Types of financial derivatives

I am looking for an explanation for different types/grades of derivatives. For example we have various asset classes: equities FX (currency) derivatives, etc. Or different types of secured debts, ...
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3 votes
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How to monetize ability to predict small stock movements smaller than spread?

For a relatively small subset of stock symbols I have been able to build a model that is able to 20-100 times per day consistently predict whether a stock is going up within the next 2 minutes, being ...
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0 votes
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Valuing Long-Term (5+ year) Cliquet Options

I'm trying to figure out how to value long term equity cliquet options with expirations 5+ years out. Even for SPX cliquets, vol surfaces are from what I can tell non-existent. Where would someone get ...
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2 votes
0 answers
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Average Strike Option with bounds

I'm looking to price a call option with an exotic feature. The price I'm trying to calculate at time $t=0$ is \begin{equation} C = E^\mathbb{Q}[(S_T-K_T)^+] \end{equation} where $S_t$ is the stock ...
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  • 1,048
1 vote
2 answers
131 views

Deltas on Barrier options vs Vanilla options

In "Heard on the Street" it states that $$\Delta_{\text{up and out call}} \leq \Delta_{\text{standard call}} \leq \Delta_{\text{down and out call}}$$ Is there an intuitive explanation for why this ...
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  • 2,131
0 votes
3 answers
473 views

Formula for the discounted payoff of a digital option

In "Heard on the Street" it states that the expected discounted payoff of a digital option is $$H\exp^{-r(T-t)}N(d_2)$$ where $H$ is the payoff of the option, the exponential is the discounting. ...
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  • 2,131
1 vote
0 answers
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Proving an Expectation

Assume the risk-free bond $B_t$ and the stock $S_t$ follow the dynamics of the Black & Scholes model without dividends. Consider the perpetual American put option with payoff $(K-S_\tau)^+$ when ...
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2 votes
1 answer
275 views

Floating Strike Lookback Call Option

Assume the risk-free bond $B_t$ and the stock $S_t$ follow the dynamics of the Black & Scholes model without dividends (with interest rate $r$, stock drift $\mu$ and volatility $\sigma$). If $r=\...
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Exotic Derivatives Model Calibration

Suppose if we will like to price an exotic option with a model,we calibrate them to natural hedging instruments that are available in the market. Do we use all the instruments as hedge or only a ...
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1 vote
0 answers
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Pricing exchange options

I am really puzzled about the mechanism of pricing of exchange options using a change in numeraire: Suppose that $S^{(1)}$ and $S^{(2)}$ are stocks satisfying SDEs $$dS^{(1)}_t = \mu_1 S^{(1)}_t \,...
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what is the state of the art method for hedging barrier options?

I want to create my own Barrier options for some security, I want to trade. I did some literature review, and found a static replication method, and many dynamic replication methods. I want to know ...
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