Questions tagged [exotics]
The exotics tag has no usage guidance.
1
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0answers
72 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
85 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
233 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
71 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
168 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
166 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
324 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
votes
2answers
388 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
126 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
318 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
215 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
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1answer
62 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
65 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
40 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
237 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
272 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
36 views
Boundary condition of lookback option
This is a well know conclusion of the boundary condition of lookback option. Here
$$\dfrac{d S_t}{S_t} = (\mu - D)dt + \sigma ...
3
votes
1answer
163 views
How to price the American style Asian option with recent N day average
How to price the American style Asian option with recent N day average, for example, we exercise at t day, then the payment is
$$...
-4
votes
1answer
167 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
$$d X_t = (\mu_x - D_x)X_t dt + \sigma_xX_td W^x_t$$
$$d Y_t = (\mu_y - D_y)Y_t dt + \sigma_yY_td W^y_t$$
$$d W^x_td W^...
2
votes
1answer
194 views
Gamma of a Lookback Option
From this book, http://docs.finance.free.fr/Options/Exotic_Options_Trading.pdf,
it states that
The gamma profile of a Max lookback option becomes intuitive when
viewing it as a ladder option. ...
2
votes
1answer
131 views
How to solve one-touch American call
I want to solve the one-touch American call at $t = 0$ with level $B,$ maturity $T$ under the following assumption:
$$d S= rSd t + \sigma SdW,\quad S_0<B.$$
We have following formula:
$$V(S_0,0) = \...
1
vote
1answer
252 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
155 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
$$Q_t+\dfrac{1}...
3
votes
1answer
79 views
Is there a quick way to see why this claim $C(S, t)$ on $S$ does not satisfy the Black-Scholes PDE?
I'm self-studying for an actuarial exam on financial economics and encountered the below practice exam problem.
An exam problem should typically take 5-6 minutes to complete, so I'm wondering if ...
1
vote
0answers
210 views
Risk management for Digital Option at large Bank
Say, an investment bank sell Digital Call Option to its client at strike 100.
But trader at the bank want to book the deal with a call spread at 99/100 (price&hedge Digital Option like price&...
1
vote
1answer
222 views
PDE of barrier and lookback options
In Shreve's book, he obtain the PDE of barrier option by
Payment function
$$V(T) = (S(T) - K)^+\mathbb{II}_{\{S_{\textrm{max}}(T) > B\}}$$
Then use the risk neutral pricing formula and Markov ...
0
votes
1answer
46 views
Valuing a claim on $S^a$: This exercise/solution appears to have a mistake
The below exercise and solution was found in "Models for Financial Economics" by Abraham Weishaus. My issues are:
In this problem, $S(t)$ does not satisfy the Black-Scholes framework because ...
4
votes
1answer
152 views
Is the asset-or-nothing call option in this example valued incorrectly in the Black-Scholes framework?
I understand the solution to the author's example below, but I can't help but notice that the implied volatility is an imaginary number:
The time-$t$ price of an All-or-nothing Asset Call is $S_t e^{-...
-1
votes
1answer
48 views
Clarification on the payoff of a portfolio consisting of a long Up&In Put and short Up&In Call
I am trying to make sense of this example:
I'm not following the second line in red: "If you buy an up-and-in put and sell an up-and-in call, the payoff is the strike price minus the stock price ...
1
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0answers
193 views
Pricing Exotic options
I am stuck at a assignment problem where I have to compute the price of an exotic option.
I am given the values the prices of option $C(X;k) = E[max(0,X_T - k)]$ for different strike prices $k$ and ...
11
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2answers
2k views
Delta-Hedging Exotic Options
I have already figured out that Delta-hedging essentially turns European options into volatility products where you pay implied vol and get paid realized vol for long positions and you pay realized ...
3
votes
2answers
3k views
hedging barrier options
Consider Black Scholes dynamics for the stock price
$$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
113 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
252 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 ...
4
votes
1answer
4k 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
138 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
172 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
774 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 ...
3
votes
1answer
539 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
363 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
675 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
186 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 ...
0
votes
2answers
625 views
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 ...
2
votes
3answers
206 views
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}{...
4
votes
3answers
6k views
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, ...
4
votes
2answers
1k views
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 ...
2
votes
1answer
58 views
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 = \...
