Questions tagged [exotics]
The exotics tag has no usage guidance.
89
questions
1
vote
2answers
70 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 ...
0
votes
3answers
51 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.
...
1
vote
0answers
63 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
votes
1answer
154 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=\...
1
vote
0answers
55 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 ...
1
vote
0answers
54 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
$$dS^{(1)}_t = \mu_1 S^{(1)}_t \,...
2
votes
0answers
44 views
what is the state of the art method for hedging barrier options?
I want to create my own Barrier options for some security, I want to trade. I did some literature review, and found a static replication method, and many dynamic replication methods. I want to know ...
3
votes
0answers
51 views
What models are used for pricing cliquet options (esp. for Asian Equity underliers)? How good is Bergomi model?
What are the most common models, actually used by trading desks for Asian underliers, for pricing cliquet options?
I would like to know both - (1) the production model used for daily P&L, and ...
2
votes
0answers
70 views
Kingdom of Denmark Nikkei put warrants
I have read in a book from Emanuel Derman that Goldman Sachs manufactured a derivative in the early 90's that consisted of buying cheap puts on th Nikkei index (and paid in Yen), combined them which a ...
2
votes
0answers
34 views
Dimension reduction for worst of basket on $min(S_1, S_2)$
Suppose we want to price an exotic equity which is a function of $min(S_1, S_2)$. To do this, I'm trying to compute an implied volatility surface for $min(S_1, S_2)$ and then price the option using ...
2
votes
1answer
75 views
Hedging an option on a non-traded asset in BS world
I have given the following task given.
Suppose you are in a Black-Scholes World where you have the standard assets
$$ dS_t = \mu S_t dt + \sigma S_t dW_t $$
$$ dB_t = r B_t dt $$
and now you also ...
2
votes
1answer
212 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
votes
1answer
106 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
votes
0answers
73 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-...
3
votes
0answers
49 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 ...
0
votes
0answers
30 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
votes
1answer
240 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: ...
1
vote
0answers
53 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
vote
1answer
45 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
votes
2answers
163 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
votes
1answer
177 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) ...
0
votes
1answer
54 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
votes
1answer
102 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 ...
1
vote
1answer
84 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
votes
1answer
93 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 "...
1
vote
0answers
68 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
votes
2answers
132 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
votes
1answer
103 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
votes
0answers
628 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
votes
0answers
157 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
votes
2answers
405 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
votes
0answers
113 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
votes
2answers
342 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
votes
0answers
299 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 \...
1
vote
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 ...
7
votes
2answers
704 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
votes
1answer
262 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
votes
1answer
570 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
votes
2answers
274 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 ...
1
vote
1answer
117 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
votes
1answer
100 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}$$
a) ...
1
vote
1answer
43 views
Verify the accuracy of a model for exotic option if there is no enough data of market price every?
How to effectively verify the accuracy of a model(may be complicate) for exotic option, if there is no enough data of market price? Is there any related reference?
1
vote
1answer
406 views
Pricing for an Odd Type of Asset or Nothing Option
Trying to derive the pricing function for a derivative on two assets $S^1$ and $S^2$ with the following payoff function:
$$\Phi(S^1_T,S^2_T)=S_T^1 \, \unicode{x1D7D9}\{S_T^2\le K\}$$
where I'm ...
0
votes
1answer
500 views
Finding the delta and gamma with historical data
I have a complicated product with knock-out barriers combined with other exotic options. I am curious if there is a fast and loose way to figure out the delta, gamma, rho, theta and possibly vega, ...
1
vote
0answers
58 views
Boundary condition of lookback option
This is a well know conclusion of the boundary condition of lookback option. Here
$$\dfrac{d S_t}{S_t} = (\mu - D)dt + \sigma ...
2
votes
1answer
209 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
$$...
-3
votes
1answer
302 views
Increasing the correlation of two asset reduce the value of spread option.
We know the payment function of Spread option is
$$\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
votes
1answer
313 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. ...
2
votes
1answer
178 views
How to solve one-touch American call
I want to solve the one-touch American call at $t = 0$ with level $B,$ maturity $T$ under the following assumption:
$$d S= rSd t + \sigma SdW,\quad S_0<B.$$
We have following formula:
$$V(S_0,0) = \...
1
vote
1answer
372 views
Hedge variance swapping by vanilla option(constant vega portfolio against underlying asset)
One book said hedging variance swaps
$$I= \sqrt{\dfrac{1}{t}\int^t_0\sigma^2(S,t)}d t$$
by vanilla option，say value $V(S,E;\...
