Questions tagged [exotics]

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28 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 ...
2
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0answers
57 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
79 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
64 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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0answers
64 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 ...
2
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1answer
167 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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0answers
56 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
59 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 \,...
2
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0answers
49 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 ...
3
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0answers
54 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 ...
2
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0answers
85 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 ...
2
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0answers
35 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 ...
2
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1answer
81 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 ...
2
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1answer
316 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 ...
2
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1answer
128 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 ...
2
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0answers
76 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-...
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0answers
54 views

Rainbow option pricing formula under *Bachelier* model

Let's consider a call on min option on two underlying arithmetic Browniation motions $V_t$ and $H_t$ (no drift). Let $P_t$ denotes the price process of the option, $r$ the riskfree rate, $\tau$ the ...
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31 views

How does the implied correlation change when the spot price of the Basket Call/ Put option goes up?

Given a basket Call/Put: $BasketCall_{payoff} = max[0, \Sigma^n_{i=1} w_iS_i(T) - K]$ If the spot price of the basket goes up/down, how would the implied correlation change? I guess what I am not ...
5
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1answer
262 views

Exotic Trading Basic Questions - Banking

I just joined a support team for an equity exotic trading desk in a bank, I am looking for a high level overview of how exotic trading works in a bank. For my questions let's take a common product: ...
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0answers
58 views

Swaption pricing and strategies

I am looking for resources (books, papers, websites, etc.) that deal with Vanilla and Exotic swaptions from a more advanced and quantitative perspective. I am interested in both the pricing side (e.g. ...
1
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1answer
46 views

In search of double barrier out option on a BM

We have a BM $X_t$ with $dX_t=\sigma dB_t$ ($X_0$ not necessarily zero!) under the risk neutral measure $\Bbb Q$. Given upper barrier $U$, lower barrier $L$, "strike" $K$ such that $L<X_0<U, L&...
2
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2answers
211 views

What is the best book to learn about local vs. stochastic volatility, modelling and pricing of Exotics?

I am starting to delve into the world of Exotics and I am trying to find a rigorous yet understandable book that covers both mathematically and qualitatively (especially mathematically) the following ...
5
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1answer
194 views

How frequently is local volatility calibrated to implied vol surface, in practice?

This has two related questions - How frequently do equity derivative traders re-mark the implied volatility surface - (i) once a day (e.g. at start of trading day, or end-of-day), or (ii) ...
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1answer
68 views

Multi-legged Swap pricing

can anyone guide me how to price a multi-legged swap and whether I need Monte Carlo / LMM based approach or if there is a closed form solution. Receive leg "Libor 3m +1%" Payment leg If Libor is ...
2
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1answer
120 views

Why do we have to use in-the-money paths in LSMC, and how?

In Longstaff's original LSMC paper (Valuing American Options by Simulation: A Simple Least-Squares Approach, 2001 (link)), it is claimed that one should only use in-the-money paths for regression at ...
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1answer
94 views

How to hedge x gamma in callable prdc?

How do you hedge the short rates - fx cross gamma in a callable PRDC (Power Reverse Dual Currency note) ?
2
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1answer
95 views

Finite difference methods for (continuously) strike-resettable American options

For simplicity, let us consider an American call/put with a continuously resettable strike price. Current time is $t=0$, maturity is at $t=T$, and the initial strike is $K_0$. We consider a "...
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0answers
71 views

Pricing an exotic with barrier at discrete times

How would you price the following option on underlying $S$ without dividends? Time to maturity of option $\tau = 12$ months Option has a strike $K > 0$ and constant barrier $B > 0$. $t_0$ is ...
2
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2answers
141 views

Is it possible to model path-dependent clauses using finite difference methods?

I'm trying to build a convertible bond pricer. In my case a convertible bond is a complex derivative with call, put and conversion price reset clauses, and all of the clauses are triggered in a path-...
7
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1answer
139 views

Quanto basket payoff

I have a payoff that is the worst of the returns two indices: S&P500 (SPX) and Euro Stoxx 50 (SX5E). $\pi = \min \left\{\left(\frac{\text{SPX}_\tau-\text{SPX}_0}{\text{SPX}_0}\right),\left(\frac{\...
2
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0answers
691 views

Cash-or-nothing and Asset-or-nothing price derivation

I was wondering how to derive the price of a cash-or-nothing and asset-or-nothing option by trying to work out the expectation under the risk-neutral measure, while assuming that the underlying ...
2
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0answers
170 views

Exotic derivatives - Replication

I would like to replicate the payoff Max(0, Min(S1, K) - S2) with a combination of the following derivatives: -> option on S1, strike of our choice -> option on (S1-S2), strike of our choice -> A ...
4
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2answers
425 views

Pricing and hedging fund-linked derivatives

I am looking for info regarding pricing, and hedging (notably vega and delta) of derivatives on funds. Could you please confirm/complete the below information I believe I've understood so far, or ...
2
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0answers
115 views

Barrier Option with Time-Dependent Rebate

Is there a closed form solution for American Single-Barrier Options (specifically Down-and-Out Calls) which undergo linear principal amortization based on the amount of time passed before being KO'ed? ...
3
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2answers
379 views

Flaw in the following argument with Binary Options and Skew

A Binary option is ATM and expires tomorrow. If the skew of the vanilla options steepens (left side up, right side down) what happens to the price of the Binary Option. I know that using a ...
2
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0answers
306 views

Pricing of multi strike rainbow options

I am looking at the pricing of a two asset multi strike option in the Black Scholes framework but I am struggling with coming up with a pricing formula. The payoff of the option at maturity is \...
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1answer
1k views

Autocall replication using vanilla options

How to replicate a single asset auto call through call spreads ? Single asset auto call: Definition and pay off profile is clear. Just want to know the method to replicate it through vanilla call ...
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2answers
768 views

Multithreading Monte-Carlo pricing in QuantLib for a single product

I've been actively using QuantLib for structured product pricing using Monte Carlo. Due to the fact that at a great deal of paths are often needed and one needs to speed up the calculation and all ...
3
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1answer
293 views

Floating Strike Lookback Delta Risk

I'm running through some delta hedging simulations of floating strike lookback call options (that is, I'm short the options) during a volatile (downside) period for the underlying and some very odd ...
2
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1answer
595 views

Barrier option with Rebate

Can I use the Implied vol surface from the plain vanilla options to price the Knock out Barrier options with Rebate?. In addition, for risk management purpose, can I just imply the volatility from the ...
3
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2answers
284 views

What Positions on an Underlier CANNOT be Hedged with Vanillas?

Say I have infinite precision of strikes $K$ (continuous world $dk$) and expirations $T$ (continuous $dT$) all with liquidity (so no practical limitations). What positions in an underlying can't be ...
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1answer
124 views

Price of the form $v(t,x)=\phi(t,T)x^n$ for a power option

I'm trying to solve the next exercise: Let $g(S_{T})=S_{T}^{n}$ be the pay-off of a power option. Show that it's price is given by $v(t,x)=\phi(t,T)x^{n}.$ Find the function $\phi(t,T)$ using risk-...
2
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1answer
105 views

Pricing and Arbitrage of Inverse Asset Claim

I'm working through the following little exotic exercise and have some questions and curiosity as to whether I'm on the right track Consider the claims $$Y_t=\frac{1}{S_t}$$ $$X=\frac{1}{S_T}$$ a) ...
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1answer
44 views

Verify the accuracy of a model for exotic option if there is no enough data of market price every?

How to effectively verify the accuracy of a model(may be complicate) for exotic option, if there is no enough data of market price? Is there any related reference?
1
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1answer
418 views

Pricing for an Odd Type of Asset or Nothing Option

Trying to derive the pricing function for a derivative on two assets $S^1$ and $S^2$ with the following payoff function: $$\Phi(S^1_T,S^2_T)=S_T^1 \, \unicode{x1D7D9}\{S_T^2\le K\}$$ where I'm ...
0
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1answer
524 views

Finding the delta and gamma with historical data

I have a complicated product with knock-out barriers combined with other exotic options. I am curious if there is a fast and loose way to figure out the delta, gamma, rho, theta and possibly vega, ...
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0answers
59 views

Boundary condition of lookback option

This is a well know conclusion of the boundary condition of lookback option. Here $$\dfrac{d S_t}{S_t} = (\mu - D)dt + \sigma ...
2
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1answer
211 views

How to price the American style Asian option with recent N day average

How to price the American style Asian option with recent N day average, for example, we exercise at t day, then the payment is $$...
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1answer
309 views

Increasing the correlation of two asset reduce the value of spread option.

We know the payment function of Spread option is $$\max\{X_T - Y_T-K,0\}$$ here $$d X_t = (\mu_x - D_x)X_t dt + \sigma_xX_td W^x_t$$ $$d Y_t = (\mu_y - D_y)Y_t dt + \sigma_yY_td W^y_t$$ $$d W^x_td W^...
2
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1answer
325 views

Gamma of a Lookback Option

From this book, http://docs.finance.free.fr/Options/Exotic_Options_Trading.pdf, it states that The gamma profile of a Max lookback option becomes intuitive when viewing it as a ladder option. ...