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.

3
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0answers
142 views

Early Exercise Options and Coin Flipping

This problem was presented in an interview, and I know I got it roughly correct. But I am still not entirely understanding the early exercise component of it: Say I am advertising a game where I ...
4
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0answers
68 views

Is there an arbitrage free option model that treats volatility as a deterministic function of strike?

I am trying to get a good understanding of the different models out there, and thus be able to study hedging errors, and strengths and weaknesses. My understanding of the Local Volatility model in ...
1
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0answers
43 views

Put call symmetry of put

I hope this is a simple question but I just wanted to get confirmation and also the intuition behind it. I know the put call symmetry and I often see it expressed as: Call(S, K) = Put(K, S) = K/S Put(...
1
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1answer
54 views

Deriving the risk neutral probability with the arrow debreu Price vector

today I had an oral exam about Stochastic Finance. With one of the questions I was pretty helpless. We were talking option pricing in a scenario where we have Portfolio with n-assets and k-states. But ...
3
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1answer
954 views

FX Option strikes from ATM, RR, BF quotes

I am trying to replicate the results in Consistent Pricing of FX Options, A. Castagna and F. Mercurio. However, when I calculate the strike prices for 25-delta put and call and ATM I cannot get the ...
0
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0answers
41 views

Free Call Option [duplicate]

Suppose we follow the assumptions of the Black-Scholes Model, including unlimited borrowing, continuous prices, and frictionless markets. For simplicity assume the risk-free rate is 0. In this world, ...
2
votes
1answer
98 views

What's the logic behind binomial model ups and downs?

I want to understand what is the underlying logic in the calculation of u and d in a binomial model. $$ u = \exp\Bigl(\sigma \sqrt{\Delta t} \Bigr), \quad d = \exp\Bigl(-\sigma \sqrt{\Delta t} \Bigr)...
0
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1answer
124 views

How is FX cross rates options are priced?

Say I have market for EUR/USD and also USD/CAD, how would EUR/CAD would be priced and hedged in practice? What are good papers/book chapters to read on that? (Assuming basic knowledge already on ...
1
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1answer
261 views

Exercise Probabilities Vanilla Cap/Foor

When looking at the discounted pay-off formulas of a vanilla caplet and a vanilla floorlet $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_k-r_{cap},0)$ $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_{floor}-...
2
votes
1answer
192 views

What are some beginner quantitative option trading strategies?

I'm new to quantitative trading, with good knowledge in finance and coding (mainly Python, Java, R, etc). I would like to know if there are any basic quantitative option trading strategies that can ...
0
votes
1answer
191 views

Basic Replication of European Call Option

I am looking at the very basics of replicating an option with a portfolio of risky and risk free assets. As such we can define a portfolio of $x$ no. of shares, $y$ bonds & $z$ options at time $(T)...
0
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1answer
67 views

Solving for Implied Volatility Vega gets stuck at 0 (Python)

So my goal is to calculate option greeks with as few manual inputs as possible. I managed to get the IV for at the money options but then when I try further OTM strikes my results get completely ...
1
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2answers
1k views

Call and Put Prices Equal at Forward Price - Why?

Consider a European call and put with values $C_t$ and $P_t$, respectively, under the Black-Scholes model. By put-call parity, $$ C_t - P_t = S_t - Ke^{-r(T-t)} $$ for expiration time $T$. Note if $...
2
votes
2answers
139 views

What is “Lambda” in Heston's original paper on stochastic volatility models?

In his paper (link), he has the equations: b1 = k + ƛ - (ρ * σ) b2 = k + ƛ k is the rate of mean reversion, ρ is the correlation between the two Wiener processes, σ is vol of vol, what is ƛ? ...
0
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0answers
33 views

Binomial model option

An American call option with exercise price $K = 90$ written on an asset where the asset prices in dollars are given below, the interest rate per period is zero, and a dividend of $5$ is paid between ...
2
votes
1answer
91 views

Why Can I not estimate a CVAR from Heston Model

I fit the parameters of Heston model, using option data for SPX. Now I have the process S and P 500 is expected to follow. I make 100,000 simulations of this process and then calculate the expected ...
3
votes
1answer
99 views

Which securities have expirations more often than monthly?

I'd like to explore buying low-cost calls close to the money, so I'm looking for low time values in options premiums. This happens near options expiration. Unfortunately, most options expire on the ...
2
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2answers
80 views

American Option Exercise

Suppose I am a market maker in American options. At end of day I have positions in various options but my portfolio is overall hedged. Now, after the market close, someone decides to exercise an ITM ...
4
votes
1answer
98 views

Is there a simple, intuitive derivation (using Taylor series) of the following approximation to Vega-weighted Implied Volatility?

The approximation is: $$\sigma \approx \frac{\sum V_j\sigma_j}{\sum V_j}$$ Background information from the first answer to this post: "Say that you have a portfolio of options with prices $P_j$. ...
2
votes
1answer
84 views

Derivatives Trading Jargon

Could you please help to understand trading jargon in this tweet. Thanks in advance. For non twitter users: Bookie pushing 5-delta (strike of 8) 2 month TRY puts. 0.6%
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1answer
138 views

How to show arbitrage when a European option price is greater than the no-arbitrage price?

My example is: Current price = 20, If it goes up it'll be worth 22, if it goes down it will be worth 18 risk free rate: 12%, time = 3 months Strike = 21 call option is worth 0.633 I know that if the ...
34
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5answers
65k views

How can the implied volatility be calculated?

We all know if you back out of the B.S. option pricing model you can solve for what the option is "implying" about the underlyings volatility. Is there a simple, closed form, formula deriving Implied ...
1
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0answers
24 views

Where to Find Foreign Countries Index Option Data

OptionMetrics database contains option data for several US indexes (SP500, SP100...). But I don't see any option data for foreign indexes. Is there a place from which I could get/purchase the options ...
1
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0answers
63 views

Geometric Brownian Motion with Dividends

I am working on a problem and had a quick question. I understand that for Geometric Brownian Motion we use the formula: $$X_{t_n} = X_{t_{n-1}} + \mu X_{t_{n-1}} \Delta t + \sigma X_{t_{n-1}} \...
2
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0answers
49 views

Risk-Neutral Pricing with Regime Switching

As the title suggests, I am currently trying to implement a dual regime-switching options pricing model. In its simplest form, I am fitting a risk-neutral GARCH(1,1) to a crash and normal regime. ...
1
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1answer
476 views

Differences between Snowball, KIKO and TRF derivatives?

Can you explain what are some similarities and differences between snowball, KIKO (knock in knock out) and TRF (target redemption forward) derivatives?
5
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1answer
112 views

Pricing in the Heston Model

The dynamics of the Heston Model is \begin{align*} \frac{dS}{S} & = \lambda \sqrt{\nu} d W^S \\[0.5em] d \nu & = k (1- \nu )dt + \epsilon \sqrt{\nu} dW^\sigma \end{align*} where $\lambda$...
2
votes
1answer
74 views

Static hedge for up-and-out Digital Call

I am trying to come up with a static hedge for a Digital Call with strike K that knocks out when price > barrier H. I know it will involve non-knockout digital calls with strike K and strike H but I ...
1
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1answer
53 views

Asian Options Vs Bermudan Options

Which of these options are more popular in practice/used in industry? And where exactly are they used? Also, I have been searching for listed Asian and Bermudan options, for volume data etc, but have ...
1
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1answer
71 views

Looking for a Book

I hope everyone is well. While I was looking for derivations of Greeks I came across part of a book. Could you help me to find its name please ? Here is the link: http://centerforpbbefr.rutgers.edu/...
1
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0answers
35 views

Poisson parameter in Merton's Jump-Diffusion Model to price call option

I've been taught the following European call valuation formula under jump-diffusion model: \begin{equation} price = E[e^{-rT}max(S_T-K,0)] =\sum_{j = 0}^\infty e^{-rT}P_j(\lambda)E[max(S_T-K,0)|J=j] \...
4
votes
0answers
70 views

Numerical simulation of Heston model

I am trying to simulate on Python random paths for a general asset price as described by the Heston model: \begin{equation} \begin{aligned} dS_t &= \mu S_t dt + \sqrt{\nu_t} S_t dW^S_t \\ d\nu_t &...
4
votes
1answer
45 views

Why is there no parameter for the estimated economic growth of a company in the option price model

Can someone explain me why the economic growth of a company is irrelevant in determining the option price. Especially for options with a long maturity e.g. 5 years it seems to me that for a high ...
2
votes
1answer
85 views

Black Scholes- Options and OIS

I have 2 questions. In the Black Scholes formula for currency options, where does forward premium come in? Volatility will be a historic parameter, so which component considers fwd premia. Typically,...
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1answer
49 views

How to understand firm option expiration cycle?

Here I am trying to understand the firm option expiration cycle: When I read Investopedia, it says: Most of stock options are on one of three expiration cycles, which consists of one month per ...
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1answer
186 views

Where can I get Currency options historical data?

where can I get historical data for currency options? For most part, google gives me links to binary options and other shady webpages.
0
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3answers
156 views

Options Delta Meaning of Term [closed]

not able to understand delta in options. Whilst I understand, it is how much the option moves when the underlying moves by 1 unit, I fail to understand, when someone books a currency option, why does ...
2
votes
1answer
76 views

Where can I get some Inflation Option example quotes (year-on-year and zero-coupon)

I am writing an academic paper on calibration of inflation vanilla options. I need to generate examples for the paper. Is there anywhere I can get example data for the Inflation year-on-year options, ...
1
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0answers
71 views

Fitting a forecasting S&P500 roll volatilities

I have a time series of S&P500 prices, for which I have calculated log-returns and roll-volatility. My goal is to forecast daily realized volatility and test a straddle strategy based on it (I ...
1
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0answers
99 views

Why historical volatility is calculated as N-days annualized?

Annualized historical volatility is always calculate with 10-, 20- days time window. I don't quite understand. Compare with annualized historical return, annualized historical return is never ...
6
votes
3answers
2k views

Which volatilities should I use for Quanto Options?

Quanto options pricing formula, as described in this paper is a function of two volatilities: one from the underlying asset and another from the exchange rate. How can I read the "right" volatilies ...
2
votes
1answer
84 views

Inherent volatility of selling longterm options and buying short term options

A two-month option has an implied vol of 60%, the corresponding 2-year option has an implied vol of 34%. You buy the short terms and sell the long terms. What is the inherent volatility of the total ...
6
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5answers
324 views

Heston Model Integration Oscillations

Is there a way to reduce oscillations for the numerical integration when evaluating the Heston model. I am pricing a series of 5000 options scattered over the Heston model parameter space and I find ...
1
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0answers
62 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
0answers
123 views

Fitting Gatheral's SVI model

I was considering using Gatheral's formula for fitting option skew. In the specific (commodity) market that I am concerned with, the underlying is ca. at 50, and typically 5 integer strikes left and ...
1
vote
1answer
61 views

Call Option Overvalued and put-call parity [closed]

I have a question regarding if a Call option is overvalued compared to the call price and how you can benefit from the Arbitrage opportunity. My thoughts are as follows: Step 1: Short the call ...
4
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0answers
216 views

Higher Order Greeks

In studying options pricing a while back, I had learned of the higher order sensitivities of of Speed and Color. Speed was the rate at which the gamma changes with the underlying. Color is a ...
29
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4answers
20k views

How to derive the implied probability distribution from B-S volatilities?

The general problem I have is visualization of the implied distribution of returns of a currency pair. I usually use QQplots for historical returns, so for example versus the normal distribution: ...
4
votes
3answers
509 views

use Monte Carlo or FDM to price Basket option

In the real practice, do we use Monte Carlo or finite difference method of PDE to price the ...
4
votes
2answers
192 views

Replicating the square of an option $C^2 (S,K,t,T)$

Given a vanilla options market, i.e. $C(S,K,t, T)$ for all strikes $K$, is it possible to replicate $C^2 (S,K,t,T)$? So I am looking for a self-financing portfolio which has a price equal to $C^2(S,K,...