Questions tagged [options]

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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43 views

How does most Forex options work? What is the most liquid or popular type of forex options?

For the "mainstream" forex options for example those (in the size of bn) posted on this site: https://www.forexlive.com/orders/!/fx-option-expiries-for-thursday-july-02-at-the-10am-ny-cut-...
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Higher moments of a straddle

Following the logic of Ben-Meir and Schiff (2012) and this question the first, second, third and fourth raw moments of a put are: Similarity, for a call it is as follows: where and ...
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What is the simplest form under which this hybrid can be epxressed?

I would like to price this \begin{equation*} \mathbb{E}^{\mathbb{Q}} \left[ e^{-\int_{0}^{T} r_{s}ds} f \left( CMS_{T_f}, S_{T_f} \right) | \mathcal{F}_{0} \right] \end{equation*} with the least ...
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2answers
602 views

“The potential gain of a Call Option is always incorporated in the Option's price” - Why is that?

I've heard this but I don't understand why. The demonstration of this is that the Ask Price of a Call Option is always higher than the difference between the Strike Price and the price of underlying ...
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2answers
121 views

Effect of correlation on a best-of rainbow option

EDIT 2: I found the problem(s) and the prices seem to behave as expected now. For anyone interested there was a bug when normalizing the dependant ranom normal variates used in the simulation, so ...
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2answers
256 views

Why are interest supposed deterministic for equity?

I don't see why would rates be considered as deterministic when trying to price $\mathbb{E}^{Q} \left[ e^{-\int_{0}^{T_{f}}r_{s}ds} \left( S_{T_f} \right) | \mathcal{F}_{0} \right]$ I would like to ...
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45 views

Free or cheap data source for the current European Options prices?

Is there a free or cheap (<15$/month) data source for the current (not historical) for European Options? Something like Yahoo Finance option page, with option chain contract prices. It's ok if it's ...
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1answer
74 views

Compute the price of a derivative which pays $\log(S_T)S_T$ in the Black Scholes world

Compute the price of a derivative which has pays $\log(S_T)S_T$, you can assume that the Black Scholes model is valid. Using the stock measure we can write the expectation as $$D(0) = S_0 \mathbb{E}...
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4answers
221 views
+50

Find a formula for the price of a derivative paying $\max(S_T(S_T-K),0)$

Develop a formula for the price of a derivative paying $$\max(S_T(S_T-K))$$ in the Black Scholes model. Apparently the trick to this question is to compute the expectation under the stock measure. So,...
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38 views

What is the typical work-flow and skills/techniques required for someone working on Structuring Products?

Are there any Portfolio Optimization techniques (Markowitz, Prospect Theory, etc...), valuations and derivatives hedging techniques? What is a typical workflow and what should one master?
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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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3answers
107 views

Price of Call Option with or without jumps

Suppose two assets in Black Scholes world have the same volatility, but one has downward jumps at random times. How does this affect the option prices? I would have thought that downward jumps would ...
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2answers
908 views

Which is riskier: a call option or the underlying?

From Joshi's Quant Interview Questions and Answers: What is riskier: a call option or the underlying? (Consider a one day time horizon and compute which has bigger Delta as a fraction of value). I ...
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1answer
47 views

FX pricing replication

Pay in currency : cur The FX is : $FX^{cur_2/cur_1}$ European options on the FX (and itself) are quoted in currency cur 1. I'm looking for the price of \begin{equation*} \mathbb{E}^{Q} \left[ e^{-\...
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2 Equity with different currencies and different fixing dates

Given Pay in currency : cur european options on the underlying 1 (and itself) are quoted in currency 1 with fixing date 1 european options on the underlying 2 (and itself) are quoted in currency 2....
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Dispersion Trading with a 2 component index

I have a dispersion question I need help with...An index SPY has only 2 components - AAPL and AMZN. We are given the implied volatility of SPY and AAPL as well as the correlation between the 2 assets. ...
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1answer
81 views

Simple approach to interpolate option surface

Let's set the spot price as 1 (spot price of underlying security) and express each option contract as a point in 3D space $$ \{ x, y, z \} = \{ tenor, moneyness, premium \} $$ where the premium is ...
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1answer
58 views

liquidity of a portfolio of options

In the asset management industry, many reports contain liquidity metrics such as the no. of days to liquidate 95% of a position, based on a certain participation rate. If that position is a stock or a ...
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1answer
47 views

Why my delta position is increasing with increase in spot?

I am trying to take position in future as per the delta position of short put. My strike is 13794 for short put option, spot 10305.3 and volatility is 20.153 then I am getting 5890 position to buy and ...
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0answers
53 views

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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1answer
31 views

Delta-normal VaR of portfolio of stock and call option

I have to calculate the 10-day 99% VaR of a portfolio that consists of a portfolio of 260 stocks of a company $K$ and that is short 500 call (European) options of the same company. I know that the ...
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1answer
50 views

Implied volatility of hypothetical options market

I am attempting to create a volatility surface for a US electricity market that has a liquid futures market but nearly non-existent options market (<5 trades per month across all strikes and ...
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Can option chain data be used as a quick and dirty substitute for proper pricing calculations for non-traded options?

I wonder if the option chain data that is published everyday by websites like Yahoo finance can be used to quickly price options that are not yet traded? So in other words, to estimate option prices ...
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1answer
45 views

Is there a sound logic for buying a portfolio of call options in the same ratio as you would buy the underlying shares?

Suppose I believe it would be profitable to build an investment portfolio by investing, say, USD 30,000 in stocks in the following ratio: 30% in shares of CompanyA, 30% in CompanyB and 40% in CompanyC....
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1answer
60 views

Kurtosis of a straddle

I want to determine the kurtosis of a straddle. My question is closely related with the following topic here. According to the following paper of Ben-Meir and Schiff (2012) the expected value of a ...
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2answers
87 views

Calculating Implied Volatility from a put option

I am trying to find the Black-Scholes implied vol from a put option. I know how to do this in the case of a regular put option on an underlier $S(t)$ where $$ p(t, K) = e^{-r(T-t)}\mathbb{E}_Q\Big[ (K ...
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2answers
77 views

How does high IV effect a put backspread?

I have a hard time understanding how high IV effects the amount of gamma obtained via a put backspread. Is it via the angle on the payoff or via the ratio one gets i.e number of OTMs one can buy? or ...
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43 views

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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0answers
25 views

Does equity premium puzzle affect option-implied RWDs using Arrow-Debreu equilibrium?

I am researching and learning about option-implied RNDs (risk neutral densities) and transformation to RWDs (risk world densities) using expected utility theory to compute risk aversion values. This ...
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42 views

R: How do i finish the tails in the risk neutral density, obtained from option prices

Im currently working on constructing the risk neutral probability distribution of a stock, based on the option prices. In doing so, i calculate the implied volatilities from the option prices, and ...
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2answers
90 views

May someone please explain the intuition behind the Black-Scholes Equation?

Consider the Black-Scholes equation for a European Call Option, \begin{equation} \begin{cases}\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + r\frac{\...
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1answer
111 views

How to find characteristic function in Fourier Cosine method (COS method) by Fang and Oosterlee

Fang and Oosterlee (2009) introduced Fourier-Cosine method (COS method) in their paper. The formula to price an option is approximately $$e^{-r\Delta t} \sum_{k=0}^{N-1}' Re\left\{ \phi\left( \frac{k\...
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1answer
70 views

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 ...
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0answers
48 views

Options pricing model inversion

He cited about Roll's compound formula for finding the lead-lag effects between stocks and options. I have a similar data for National Stock Exchange's Index, NIFTY but it's daily, not intra-day. I ...
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2answers
78 views

lead lag relationship among futures, options and stock prices

I have the data of past 10 years of NIFTY (the National Stock Exchange of India) stock, futures and options and I want to show the lead-lag relationship (which reacts first, futures, options or stocks)...
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2answers
157 views

How much money would it take to artificially inflate/depress a stock?

Please include links or at least keywords to research papers if possible. This is basically an investigation into max pain / stock pinning and what it would take for a hedge fund to cause it. Some ...
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1answer
61 views

Under what conditions will both European and American put options worth the same?

It is well-known that on a non-dividend paying stock, it is suboptimal to exercise an American call option earlier. In other words, both European and American call options on the same non-dividend ...
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1answer
78 views

Estimating optimal exercise boundary for an American call by LSM method

I'm trying to derive optimal exercise boundary using LSM method and got some weird outcome. So, I evaluated an American call option by LSM method and now need to find the optimal exercise curve. Do I ...
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How does clearing and settlement work in Europe?

I understand the basic trade lifecycle but I can't find more information on how clearing and settlement works. To my knowledge, if I buy VOD LN executed on LSE - this will be cleared by LCH which is ...
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Question about greeks and put options

I am trying to establish the relationship between put options and greeks through a general form problem. Suppose that there is a company that at market opening trades its shares at a price $p_1$.Now ...
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1answer
61 views

What are the differences between hedging with swaps, options or futures? [closed]

For instance if a bank wants to hedge against interest rate risk, it could use interest rate swaps, or options or futures contract. Or in any other example, when a manager is hedging against risks. ...
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1answer
69 views

Optimal Covered Call Strategy [closed]

How do I compute the optimal strike / expiry / when to close or roll for a covered call strategy on a highly liquid underlying (e.g. SPY)?
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2answers
83 views

Calculating the 0.50 delta strike

According to most books the ATM option is the option with a delta of 0.50. However, this is only the case when the distribution is normal. The more positively skewed the distribution, the further the ...
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1answer
90 views

Option Pricing Formula

I am really upset about an exercise, because i don't get it. Maybe someone can find my error? We are talking about a single period model. Therefore our Asset is denoted by $S(0)=1$, $U=0.05$, $D=-0....
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1answer
38 views

Digital height of an option

Could someone please help me explain the concept of Digital Height clearly in the options world? Thank you
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1answer
44 views

Foreign-Domestic Symmetry

I try to find the proof of the theorem of Foreign-Domestic Symmetry for FX options, but I did not found, Some paper or book, where it is explained? Theorem 2.1 in this paper: https://arxiv.org/pdf/...
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Stability of Finite Difference method for Breeden-Litzenberger

I am trying to derive a risk-neutral density from European call option prices using a second order finite difference scheme. Let $C(K,T)$ be the price of a European call with strike $K$ and expiry $T$ ...
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55 views

Risk-neutral probability

At period $t=0$, I have a risk free asset with price 100 with annual rate $r=5\%$ and two different stocks, $S_1$ and $S_2$, whose initial values are 100. Prices at $t=1$ are different for 3 ...
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1answer
64 views

Does Black Scholes + Stochastic interest rates result in a unique price

Black-Scholes with its assumptions results in a unique price for the call. If we introduce stochastic interest rates, would this still remain the case?
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63 views

Vega hedging swaption with caplets - precisely, what will go wrong?

I am trying to form a kind of unified perspective of how (vega) hedging an exotic with vanillas, or hedging a 'basket option' with vanillas will go wrong. So in particular, I want to be able to ...

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