Questions tagged [exotics]

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108 views

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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2answers
251 views

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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154 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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60 views

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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1answer
69 views

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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1answer
26 views

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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64 views

Black-Scholes - Security value with two sources of risk

Consider the Black-Scholes economy with two sources of risk. A security pays off $S_{1T} S_{2T}$ upon its maturity at time T, where $S_1$ is the level of the S&P500 index and $S_2$ is the price of ...
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1answer
124 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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92 views

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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1answer
121 views

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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61 views

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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39 views

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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1answer
232 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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1answer
351 views

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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1answer
1k views

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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54 views

Can the Heston model be used to price ANY option?

I've been reading through Heston's work and different Monte Carlo extensions of it and it seems very interestingly flexible. I've mainly used an application of it for pricing Memory Autocalls. Am I ...
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1answer
111 views

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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1answer
125 views

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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4answers
506 views

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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0answers
48 views

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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202 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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144 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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58 views

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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1answer
68 views

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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0answers
48 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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3answers
146 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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66 views

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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1answer
101 views

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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1answer
219 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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0answers
60 views

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 ...
2
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1answer
186 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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0answers
44 views

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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69 views

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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87 views

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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58 views

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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0answers
70 views

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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2answers
108 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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3answers
261 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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67 views

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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1answer
250 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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59 views

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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0answers
129 views

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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0answers
66 views

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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0answers
90 views

What models are used for pricing cliquet options (esp. for Asian Equity underliers)? How good is Bergomi model?

What are the most common models, actually used by trading desks for Asian underliers, for pricing cliquet options? I would like to know both - (1) the production model used for daily P&L, and ...
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0answers
161 views

Kingdom of Denmark Nikkei put warrants

I have read in a book from Emanuel Derman that Goldman Sachs manufactured a derivative in the early 90's that consisted of buying cheap puts on th Nikkei index (and paid in Yen), combined them which a ...
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0answers
47 views

Dimension reduction for worst of basket on $min(S_1, S_2)$

Suppose we want to price an exotic equity which is a function of $min(S_1, S_2)$. To do this, I'm trying to compute an implied volatility surface for $min(S_1, S_2)$ and then price the option using ...
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1answer
92 views

Hedging an option on a non-traded asset in BS world

I have given the following task given. Suppose you are in a Black-Scholes World where you have the standard assets $$ dS_t = \mu S_t dt + \sigma S_t dW_t $$ $$ dB_t = r B_t dt $$ and now you also ...
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2answers
2k views

How to price a phoenix and snowball type autocallable options?

I'm currently studying the pricing of autocallable options, especially snowball (accumalated coupon) and phoenix (accumlated coupon, but the coupon may also be autocalled if the underlying price ...
3
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1answer
378 views

Can we use Black-Scholes to price path dependent options?

I know that we can use the Black-Scholes framework to price vanilla products like a European call or put, where the payoff only depends on the share price at maturity. But can we use it to price path ...
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0answers
122 views

Bates Model Jump Percentage Parameters

I am trying to calculate the jump parameters for the Bates volatility jumps, specifically, the mean of the jump percentages, $\mu_j$. For the value of $J$, I am using jumps $|\frac{s_{i}-s_{i-1}}{s_{i-...