Questions tagged [exotics]
The exotics tag has no usage guidance.
156
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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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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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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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1
answer
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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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1
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930
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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 ...
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2
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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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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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1
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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?
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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 ...
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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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Boundary condition of lookback option
This is a well know conclusion of the boundary condition of lookback option. Here
$$\dfrac{d S_t}{S_t} = (\mu - D)dt + \sigma ...
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1
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271
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How to price the American style Asian option with recent N day average
How to price the American style Asian option with recent N day average, for example, we exercise at t day, then the payment is
$$...
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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
$$d X_t = (\mu_x - D_x)X_t dt + \sigma_xX_td W^x_t$$
$$d Y_t = (\mu_y - D_y)Y_t dt + \sigma_yY_td W^y_t$$
$$d W^x_td W^...
- 1,243
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Gamma of a Lookback Option
From this book, http://docs.finance.free.fr/Options/Exotic_Options_Trading.pdf,
it states that
The gamma profile of a Max lookback option becomes intuitive when
viewing it as a ladder option. ...
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1
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How to solve one-touch American call
I want to solve the one-touch American call at $t = 0$ with level $B,$ maturity $T$ under the following assumption:
$$d S= rSd t + \sigma SdW,\quad S_0<B.$$
We have following formula:
$$V(S_0,0) = \...
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1
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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;\...
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2
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348
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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
$$Q_t+\dfrac{1}...
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1
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Is there a quick way to see why this claim $C(S, t)$ on $S$ does not satisfy the Black-Scholes PDE?
I'm self-studying for an actuarial exam on financial economics and encountered the below practice exam problem.
An exam problem should typically take 5-6 minutes to complete, so I'm wondering if ...
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Risk management for Digital Option at large Bank
Say, an investment bank sell Digital Call Option to its client at strike 100.
But trader at the bank want to book the deal with a call spread at 99/100 (price&hedge Digital Option like price&...
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1
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PDE of barrier and lookback options
In Shreve's book, he obtain the PDE of barrier option by
Payment function
$$V(T) = (S(T) - K)^+\mathbb{II}_{\{S_{\textrm{max}}(T) > B\}}$$
Then use the risk neutral pricing formula and Markov ...
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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 ...
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1
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305
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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^{-...
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1
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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 ...
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0
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359
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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 ...
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2
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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 ...
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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 ...
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156
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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3
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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 ...
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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 ...
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1
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1k
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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 ...
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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 ...
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1
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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 ...
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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 ...
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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 ...
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How to price exotic options using Monte-Carlo?
I am actually trying to solve some exercise problem using Monte-Carlo and C++ for exotic options. Namely, the exotic options are geometric Asian options and discrete barrier option.
It is claimed ...
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Pricing exotic option whose payout depends on the stopping time
I am struggling with this question:
Let $B$ be a standard Brownian motion. In a Black-Scholes model, at time $t$, the stock price is given by
\begin{equation}
S_t = \exp \{ \sigma B_t + ( r- \frac{1}{...
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Derivation of the formulas for the values of European asset-or-nothing and cash-or-nothing options
The asset-or-nothing European option pays at t = T the value of the stock when
at time T that value exceeds or is equal to the exercise price E, and nothing if
the value of the stock is below E. So, ...
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Key Rate Duration for MBSs greater than Key Rate Tenor
Key Rate Durations (KRD) are essentially some fixed income instrument's price sensitivity to a non-parallel shift in interest rates (i.e., a shift at the "Key" Rate). For example, a 10-year bond's ...
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What different techniques exist for modeling exotics near payoff discontinuities in Finite Difference method?
If you are modeling an exotic, like a binary or a barrier, and hedging it with vanillas that have strikes quite close to the exotic's strike, then a large asset step size, for example, $\delta S = \...
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2
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PDE pricing of barrier options in BS
Path-dependent options in BS framework is intuitive to price with monte-carlo under risk-neutral measure, however it appears that several kinds can be priced with PDEs. I understand how does the story ...
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Can I trade the volume of a security or index?
Is it possible to trade a derivative product priced on the volume traded of some underlying security or index?
Does such a derivative exist on any exchange traded markets? Or anywhere?
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833
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R or Matlab code for Multi-Barrier-Options (3 or more underlyings)
I am looking for R or Matlab code examples of multi-barrier-options (or multi-barrier reverse convertibles) with at least 3 underlyings. Do you have such code or can you point me to a place where I ...
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What is the stochastic differential of a general semimartingale?
By using the canonical representation of a semimartingale in Eberlein, Glau and Papapantoleon's "Analysis of Fourier Transform Valuation Formulas and Applications", on page 3:
$$H = B + H^c + h(x) \...
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For pricing, what types of Exotic Options are suitable using Local Volatility Model or a Stochastic Volatility Model?
I understand that stochastic volatility models should be used when the exotic option payoff is volatility dependent (such as variance swaps and volatility swaps).
Stochastic volailtiy models should ...
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