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Questions tagged [exotics]

The tag has no usage guidance.

1
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1answer
32 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
69 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
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0answers
60 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
83 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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0answers
54 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{\...
1
vote
0answers
217 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
101 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
303 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
84 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? ...
2
votes
2answers
222 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
211 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
577 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 ...
6
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2answers
482 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 ...
4
votes
1answer
170 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
402 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
237 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
77 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-...
1
vote
1answer
69 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
41 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
289 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
324 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
39 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 ...
3
votes
1answer
182 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 $$...
-4
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1answer
223 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
230 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
146 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
297 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;\...
1
vote
2answers
173 views

The PDE of the probability hitting the barrier before T

Suppose: $$d S=\mu S dt+\sigma Sd W$$ $Q(t,S)$ is the probability that $S$ hit the barrier $B(S_t<B)$ before $T,$ then $Q$ satisfies following PDE $$Q_t+\dfrac{1}...
3
votes
1answer
88 views

Is there a quick way to see why this claim $C(S, t)$ on $S$ does not satisfy the Black-Scholes PDE?

I'm self-studying for an actuarial exam on financial economics and encountered the below practice exam problem. An exam problem should typically take 5-6 minutes to complete, so I'm wondering if ...
1
vote
0answers
245 views

Risk management for Digital Option at large Bank

Say, an investment bank sell Digital Call Option to its client at strike 100. But trader at the bank want to book the deal with a call spread at 99/100 (price&hedge Digital Option like price&...
1
vote
1answer
245 views

PDE of barrier and lookback options

In Shreve's book, he obtain the PDE of barrier option by Payment function $$V(T) = (S(T) - K)^+\mathbb{II}_{\{S_{\textrm{max}}(T) > B\}}$$ Then use the risk neutral pricing formula and Markov ...
0
votes
1answer
46 views

Valuing a claim on $S^a$: This exercise/solution appears to have a mistake

The below exercise and solution was found in "Models for Financial Economics" by Abraham Weishaus. My issues are: In this problem, $S(t)$ does not satisfy the Black-Scholes framework because ...
4
votes
1answer
159 views

Is the asset-or-nothing call option in this example valued incorrectly in the Black-Scholes framework?

I understand the solution to the author's example below, but I can't help but notice that the implied volatility is an imaginary number: The time-$t$ price of an All-or-nothing Asset Call is $S_t e^{-...
-1
votes
1answer
49 views

Clarification on the payoff of a portfolio consisting of a long Up&In Put and short Up&In Call

I am trying to make sense of this example: I'm not following the second line in red: "If you buy an up-and-in put and sell an up-and-in call, the payoff is the strike price minus the stock price ...
1
vote
0answers
224 views

Pricing Exotic options

I am stuck at a assignment problem where I have to compute the price of an exotic option. I am given the values the prices of option $C(X;k) = E[max(0,X_T - k)]$ for different strike prices $k$ and ...
11
votes
2answers
2k views

Delta-Hedging Exotic Options

I have already figured out that Delta-hedging essentially turns European options into volatility products where you pay implied vol and get paid realized vol for long positions and you pay realized ...
3
votes
2answers
4k views

hedging barrier options

Consider Black Scholes dynamics for the stock price $$dS_t=\mu S_tdt+\sigma S_t dW_t$$ I have "heard" it is difficult hedging barrier options if the payoff suddenly is set to zero by the boundary ...
2
votes
2answers
117 views

Does the Knock-out option price go to $0$ when the stock price goes to the barrier $B$?

I am reading Steven Shreve's book "Stochastic Calculus for Finance 2 Continuous-Time Models", page 304. My intuition is that when the stock price gets closer to the barrier, it will be more and more ...
1
vote
2answers
281 views

Pricing Exotics: Monte-Carlo is too slow?

I want to price exotic options under the exponential VG model and Merton's model to compare both models. To price exotics under Merton's model, I have written the code below. The output is the price ...
6
votes
1answer
5k views

How to simulate a jump-diffusion process?

I would like to price Asian and Digital options under Merton's jump-diffusion model. To that end, I will have to simulate from a jump diffusion process. In general, the stock price process is given ...
1
vote
0answers
148 views

Pricing with Vasicek model on basket of credit spreads

I would appreciate help with a valuation of a fixed income derivative, with an embedded exit option. Summary: Goal is to provide valuation of a fixed schedule of quarterly cash flows with an option ...
1
vote
1answer
4k views

Pricing of a Forward-start option in a Black-Scholes framework

I have read the pricing procedure of a Forward-start option in a Black-Scholes world in Musiela-Rutkowski, but I don't find their proof clear (pp. 195-6). Let me summarize their argument: Consider ...
3
votes
2answers
2k views

How is the Chooser Option's value computed in this example?

In preparation for my finals, I am attempting a question on chooser options. One question asks A European chooser option on an index ETF paying a yield of 3.0% with strike \$64 has a maturity of ...
5
votes
3answers
178 views

Basket derivatives on weather AND financial underlying?

Is somebody aware whether there exist basket derivatives whose underlyings are either related to weather (e.g. temperature) or financial indices (e.g. S&P500)? It is essential that the payoff ...
0
votes
1answer
840 views

Put-Call Parity Arbitrage Exploitation for Binary-Asset-or-Nothing Options

Is the Put-Call-Parity valid for binary (asset-or-nothing) options? If not, is there another formula for such exotic options? I know that for regular options, there are arbitrage opportunities when ...
4
votes
1answer
579 views

Feynman Kac Formula for path-dependent options

Consier geometric Brownian motion: $dS_t/S_t=\mu dt+\sigma dW_t$ Feynman Kac theorem tells us that the conditional expectation $v(t,x)=E[ e^{-rT}\Psi(S_T) | S_t=x]$ can be computed by solving the ...
2
votes
1answer
406 views

What exotic options are exchange-traded?

There are a number of exchanges that trade vanilla Call/Put American/European options on various underlyings (equities, indices, futures). There have been some trading in digital options on certain ...
3
votes
1answer
704 views

Best way to do multithread Monte-Carlo in QuantLib

QuantLib has great facilities for Monte-Carlo pricing engines, classes McSimulation and MonteCarloModel do a lot of work. But they do it in a single thread. What is best way to introduce parallel run ...
3
votes
1answer
1k views

Bloomberg scripting language (BLAN)

Did anyone work with Bloomberg scripting language (BLAN is the name I guess). If so is it really flexible and is it competitive with other valuation services (say Super Derivatives). Does it enable ...
2
votes
1answer
202 views

Pricing digital options in discrete time

I am stuck in this exercise from my textbook: Consider a one-period market model with $N+1$ assets: a bond, a stock and $N-1$ call options. The prices of the bond are $B_0=1$ and $B_1 = 1+r$, where ...