Questions tagged [exotics]
The exotics tag has no usage guidance.
149
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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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0
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105
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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
159
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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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1
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370
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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 ...
- 177
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0
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233
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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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2
votes
1
answer
368
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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 ...
- 1,875
2
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2
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232
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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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0
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98
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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, ...
- 221
3
votes
0
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106
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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 ...
- 31
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98
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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 ...
- 111
2
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83
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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 ...
- 1,096
1
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2
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253
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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 ...
- 2,472
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3
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2k
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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.
...
- 2,472
1
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0
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74
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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 ...
- 31
2
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1
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356
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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=\...
- 281
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0
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78
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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 ...
- 316
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0
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272
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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 \,...
- 642
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0
answers
92
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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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207
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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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2
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1
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418
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Kingdom of Denmark Nikkei put warrants [closed]
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 the Nikkei index (and paid in Yen) and combining them ...
- 183
2
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0
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65
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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 ...
- 387
2
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1
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108
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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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3
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5k
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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 ...
- 81
3
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1
answer
737
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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 ...
- 613
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0
answers
174
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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-...
- 111
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0
answers
133
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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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1
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1k
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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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152
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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. ...
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1
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87
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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&...
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2
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2k
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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 ...
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1
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607
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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) ...
- 986
0
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1
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217
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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
votes
1
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334
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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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1
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357
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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) ?
- 11
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1
answer
138
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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 "...
- 893
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0
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175
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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 ...
- 11
4
votes
2
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555
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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-...
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votes
1
answer
279
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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{\...
- 145
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0
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2k
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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 ...
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275
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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 ...
- 61
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2
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731
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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 ...
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0
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185
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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?
...
- 21
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2
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1k
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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 ...
- 2,472
2
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0
answers
413
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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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1
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4k
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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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2
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1k
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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 ...
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777
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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 ...
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2
votes
1
answer
898
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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
votes
2
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389
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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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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-...
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