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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1answer
87 views

Delta hedging theta pnl

Say I sell a swaption and delta hedge it, and the breakeven daily move in the underlying is $x$ bps. Then if on any given day the actual move in the underlying is $y$ bps $( y <x)$. Then I, as ...
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348 views

Risk management tools for long term Gamma/Vega sellers subject to margin calls

TL;DR: if you're a retail investor and you systematically sell long-term vertical spreads while staying Delta-neutral, your main risk comes from Vega and the Gamma of opening gaps that can throw you ...
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46 views

How should one hedge option positions on the date of expiry?

Let's say we are looking at a non-liquid equity ticker and a slightly OOM option on it. The problem is that if we buy delta to hedge it, it could move the underlying market and push the option to be ...
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52 views

Is it necessary for $P(K, t) - P(K + s, t) \geq se^{-rt}$ to hold?

Let $P(K, t)$ be a put option with strike price $K$ and expiration time $t$. Let $s > 0$. Is it necessarily true that the inequality $$P(K, t) - P(K + s, t) \geq se^{-rt}$$ holds? I know that ...
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2answers
177 views

What is the economic reason for the equality in value of an American call and European call?

In a previous question this question came up. In my mind, if I'm holding an option at time t, then there are possible future price paths where at t+k the option will be ITM but at T the option will ...
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45 views

Why not discount the dividend in the european put lower bound condition?

According to the european put lower bound condition: $ p \geq max(D + K \cdot e^{-r(t_2-t_0)} - S_0, 0)$ where $t_0$ is now and $t_2$ is maturity. Say $t_1$ is the dividend release time where $t_0&...
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80 views

Quantitative Finance books for Practitioners [duplicate]

Currently searching for some books on real options and option pricing. However, the vast majority of the books are quite theoretical, and if someone has been taught these subject in class, half of it ...
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1answer
55 views

Finding the extrinsic value of an option with conditions

Background: Consider a spread option with the payoff $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant. Let's also assume, that the correlation ...
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1answer
87 views

How does the Black Scholes Model Incorporate Log Prices Into Model?

I am still not understanding the link between log prices and how that is incorporated into the BS model. I understand why log(S) is assumed because it makes math easier and it prevents ending prices ...
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44 views

Log Contract payoff function

I can’t get where Dr. Rouah gets payoff function of log contract. Could you please take a look at that? https://frouah.com/finance%20notes/Variance%20Swap.pdf It’s on page 2, section 3. I couldn’t ...
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21 views

How to calculate a prepayment penalty on a mortgage

I have issued 2 mortgages...one with an option to prepay the loan, the other without that option. I want an objective way of calculating the extra interest rate (compared to the second) and ...
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104 views

VXX Put pricing

Last week at Friday's close, the Dec 14 37.5 Put options were selling for \$.68 with VXX at \$40.29. This week at Friday's close, the Dec 21 37.5 Put options were selling for \$.38 with VXX at \$40.50....
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20 views

Pricing a transfer option for oil

Need some input in how to attack this problem. Given are 8 timeseries: UK Oil price, Delivery Quarter 1 2020 UK Oil price, Delivery Quarter 2 2020 UK Oil price, Delivery Quarter 3 2020 UK Oil price, ...
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33 views

Using Non-Risk Neutral (Risk Natural) Parameters to Price Options?

Please correct me if any of my following statements are false. My understanding as to why we use Risk Neutral Analysis is that it makes life easy, and ultimately, allows use to come to a closed form ...
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44 views

How can I manually calculate the VAR of a call and put portfolio?

How would I solve the following question? Im unsure how to estimate the stock price using MCS.
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37 views

Understanding delta based strike selection in an Iron Condor

I am reading a small book on the proper use of Iron Condors (link). I do not use these strategies as I have had a very hard time being profitable on them. This book mentions some strategies to ...
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1answer
316 views

How could one trade volatility skew if you think it's too flat or steep?

We all know that you can trade on a forecast of volatility by dynamically hedging, but I'm wondering if there's a similar technique where in you can trade the skew specifically? Let's say you travel ...
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65 views

Kirk Spread Approximation, Greeks by Finite Difference

I am using finite difference on Kirk's Approximation for Spread Options to estimate greeks of the Spread Option. Now this is creating an problem in the estimation of gamma. For at the money options (...
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48 views

Negative vega on IR swaptions mid curve

Why do IR bermudan options have negative vega on midcurve? Does it have something to do with mean reversion and a way of lower the price vs market prices?
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4answers
277 views

How to calculate return on investment for an adjustment to a complex options position?

Say I currently hold a set of options positions with the same symbol/expiry that collectively have a net present value based on the estimated value at expiration of +10. I could also liquidate the ...
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2answers
197 views

Factor model and trading strategy in options market

We all know that there are many factor models (CAPM, Fama-French 3...) and trading strategies (momentum trading...) in equity market. I wonder whether there are any analogous factor model and momentum ...
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33 views

What adjustments need to be made to Heston model to price futures options? [duplicate]

My understanding for the Black Scholes model is that a few adjustments need to be made so that the BS model can be used to price futures. Hence the Black-76 model. What adjustments, if any, do we ...
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147 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 ...
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71 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 ...
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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(...
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1answer
60 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 ...
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994 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 ...
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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, ...
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1answer
100 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)...
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129 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 ...
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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}-...
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1answer
285 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 ...
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226 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)...
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1answer
73 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 ...
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2answers
2k 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 $...
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2answers
146 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? ...
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34 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 ...
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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 ...
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1answer
114 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 $P_j$. ...
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1answer
86 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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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 ...
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95 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}} \...
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52 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. ...
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1answer
510 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?
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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 $\lambda$...
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1answer
82 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 ...
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1answer
56 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 ...
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1answer
74 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/...
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52 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] \...
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92 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 &...