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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What does hedging a structured note mean? Whom does it benefit?

I am learning to create structured notes for clients. For a reverse convertible note with a basket of underlying equities,providing a guaranteed coupon and having a European knock-in barrier, the ...
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84 views

Deriving the solution for European call option in the Heston Model

I'm deriving the solution for European call option in the Heston Model. I follow the original paper by Heston and Fabrice Douglas Rouah's derivations in his book The Heston Model and Its Extensions in ...
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How closely does a Put's premium proxy the opposite Call's Time Value?

What are the odds of being assigned for a long dated in-the-money call option? - Personal Finance & Money Stack Exchange The math gets a little tricky here, but here's a neat trick to at least ...
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Interesting case study (risk management) [closed]

Hey where can I find an analysis of some interesting risk cases? I am thinking mainly of something related to option trading. I will be grateful for recommending interesting cases
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561 views

Implied volatility of a complex options position

Assume I have a "complex" options position like a straddle, strangle, or iron condor. In other words, several options traded together as a single position against one underlying asset (not a basket ...
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265 views

Post Trade Analysis for Option MMs

What are the kind of post trade analysis (EOD analysis) that an options market making desk does? First few things that comes to my mind are slippages and breaking the pnl into various greeks. Any ...
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Determining the early exercise curve of an American option

When I have found the price of an American option using, say, a finite difference scheme - how do I find the early exercise curve from this solution? Here is my idea: What I have is the price of the ...
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Double jumps stochastic volatility model (SVCJ, Duffie et al, 2000) - characteristic function for VIX

Currently I am working at my master's degree paper where I want to evaluate VIX options using stochastic volatility jump models.I got some MATLAB codes for the SVCJ model for the S&P, but as the ...
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Replicating portfolio

I have a doubt about the replicating portfolio methodology. Example - Consider an European Call with $K=21$ and underlying with current price $S_0=20$. We assume that, at the maturity, the underlying ...
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1answer
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Historical energy market data for European power Futures and Options?

I have been trying hard to find some historical futures and options electricity data for EEX offerings. I need the data for a model I am writing, however I have not found any free resources so far. It ...
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Call/Put Open interest difference on similar underlying

High open interest for a given option contract is an indicator for interest in that option. For that reason I wanted to take a look at how the open interest of options on volatility have evolved in ...
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Mismatch of periods with numeraire compared to the forward rates

In Joshi's The Concepts and Practice of Mathematical Finance Page 323--324 I believe that there may be a mismatch of periods with forward rates: Consider time partition $t_{0} < ... < t_{n}$ ...
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Expected Forward Volatility vs. Different Strikes

While theoretical options prices are derived from models, such as Black-Scholes, IV and IV skew reminds us that options prices are ultimately based on supply and demand. My question is the following: ...
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Collar Option K Term

I know that the value of a collar option on a stock (buy stock, buy put at $K_1$ and sell call at $K_2$) is given by $$Collar\ Value = K_1d(t,T)+Put\ Value-Call\ Value$$ My question is, why do we have ...
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259 views

Option on an Option

What is the value of the contract (to be paid at current time $t_0$) that gives one the right (but not obligation) to buy a Vanilla Call option (with certain strike K) at a pre-determined price $p$ at ...
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What's wrong with this call credit spread?

The picture below is a P&L chart for a call credit spread that exhibits the pattern I've seen in every single introduction to credit spreads I have looked at. Namely, above the long leg's (green) ...
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Help reconciling incorrect reasoning in options pricing brain teaser

I'm trying to reconcile an interesting brain teaser I was recently posed and I need help understanding the flaw in the reasoning. The problem states there is an asset which after an announcement has ...
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Writing an HFT (and not only HFT) options trading book

After finishing my PhD I came to work at one of the top market-maker in options world wide. Reason is: my master program was a lot of options pricing, but zero info on options trading, and I wondered ...
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Pairs trading on two options or option and underlying?

I have been looking into pairs trading strategies (stationary linear combination of multiple securities) for options. Multiple related options or option and underlying over small periods of time such ...
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How to use gamma theta and theta gamma ratios for managing short positions?

I'm starting to sell ATM options in order to buy the tails, and I would like to know how to use gamma/theta or theta/gamma ratio or their sum to manage and exit the short position before the gamma ...
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1answer
73 views

No-arbitrage Pricing

We have a contract whose value is $A(S_t,t) = S_t^3$ at all times, not just at expiration. $S_t$, the underlying stock, follows a Geometric Brownian Motion, $\frac{dS}{S} = \mu dt + \sigma dB$. How ...
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when deep itm european options time value increase from negative to positive

The time value of an deep ITM option usually is negative in the real world. I see deep itm options time value increase from negative to positive, why does it happen? what to expect when this happens? ...
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How is the difference between strike prices in an options chain determined?

I have been unable to find a formula, or any mention for that matter, of how the differences between successive strikes prices in an options chain are determined. It seems clear that the difference ...
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Why are Index/ETF put option volumes generally higher than the call option volumes?

It seems like put options on Index/ETFs generally have 50% more volume than call options, in terms of notionals. We don't see the same put/call volume ratios in single stocks. Why is that the case? I ...
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Binomial Model Strike Price Assumption

Let us have the standard single-period binomial pricing model, and denote the up and down states of the underlying by $S_u$,$S_d$ respectively. Let us say we have a call option on the underlying with ...
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What's the difference between a normal Autocall and a Phoenix Autocall?

I understand the structure of the autocall, how they're priced and their contingent coupons. What I'm not completely clear on is the difference between a "vanilla" Autocall and a Phoenix ...
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Why does an autocall on a linear payoff have vega?

Consider a (stochastic) linear index, say $I(t)$, in that it grows at the risk free rate (with some volatility of course). There exists a maturity date $T$ on which I receive $I(T)$; however there is ...
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Has a closed-form formula for the collateral choice option been found?

The collateral choice option problem has been formulated in e.g. Fujii and Takahashi (2011), Piterbarg (2012) or Antonov and Piterbarg (2013), as the computation of an expectation of the following ...
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202 views

How to reduce variance in Monte Carlo using Control Variates when spot prices are decreasing?

I'm trying to use the Control Variates technique to reduce the variance of the estimate obtained from a Monte Carlo simulation for option pricing. As suggested in the book by Glasserman I'm using this ...
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Monte Carlo price of European option on ZCB under Vasicek short rate

I'm trying to replicate the analytical result from the closed form Vasicek formula for European options on zero-coupon bonds using Monte-Carlo simulation. The interest rate paths I've simulated seem ...
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Why does the implied volatility on options (with the same underlying and maturity) vary? [duplicate]

Having studied the basic premises behind option pricing, I thought it would be interesting to look at some real-world options data. I found the following quotes for options on APPL: https://finance....
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Hedging in the Heston Model

I have simulated an underlying stock price, $S_t$ and a stochastic variance process, $v_t$ with the following stochastic differential equations from the Heston Universe: $$ dS_t = \mu S_tdt + \sqrt{...
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How do I request currently unavailable options to be sold?

How can I request options: for a certain stock that currently has no options traded? at a more extreme Strike Price? E.g. if I fancy buying OTM options? with a farther expiration? Does the CBOE ...
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Empirical equivalent for implied vol

Implied volatility is supposed to show volatility of the underlying over next k days where k - maturity of the option. Say our stock price is $S_t$ and percentage return is $r_t$. Then which empirical ...
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What are the most commonly used models in capital structure arbitrage?

That is, when trading stocks against bonds of the same companies.
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Neumann boundary conditions in the Schwartz mean reverting model

The Schwartz model for commodities is $$ dS = \alpha(\mu-\log S) Sdt+\sigma S dW, \quad W \text{ standard Brownian motion}$$ Let $X=\log S$, apply Ito lemma, under the equivalent martingale measure ...
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Undergraduate research topic in options [closed]

I'm an undergraduate student in finance with a pretty solid knowledge of financial mathematics and I'm currently picking a topic for my research paper this year. I have already decided I will pick ...
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Autocall pricing: what does “Lipschitz continuous parameterization” mean?

I've been reading through this research paper (A Monte Carlo Pricing Algorithm For Autocallables That Allows for Stable Differentiation by T. Alm, B. Harrach, D. Harrach, M. Keller) about a method for ...
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Modeling Basket Call Option

If I had a market basket of three assets with payouts of: q being weights. There is a correlation between each pair of daily log-stock price shocks. How would you price this call option? How would ...
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1answer
53 views

Do European call options increase in value when dividends are increased? [closed]

Say you have a call option whose current value is $4.73$ and has a $\delta = .43$. Let's say dividend is increased by $.37$. I would expect the option to increase in value by ($.43*.37$) since the ...
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Hedging a long position-one period from Steven Shreve Stochastic Calculus for Finance

The following question is taken from Steven Shreve Volume 1, Chapter 1, Exercise $1.6$ (Hedging a long position-one period) Consider a one period binomial stock model with $S_0=4$, $S_1(H)=8$ and $...
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Stochastic Interest Rates in Option pricing

My lecturer has written the slide below. The function B^T(t) is a zero coupon bond. I don't understand how V(t) can be a negative integral from 0 to ...
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Call spread hedge

I'm trying to understand how a call spread is used for FX hedging. The example that my book gives is when we have USD receivables in 12 months which we want to convert to EUR and we want to hedge ...
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Value of Call Option as Volatility goes to Infinity

Why would the value of a call option go infinity as volatility goes to infinity? I understand how you could solve this question by taking $\sigma \rightarrow \infty$ in the solution to the black ...
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Is there an all Java options-pricing library (preferably open source) besides jquantlib?

I am looking for an all-java implementation of black scholes, preferably open source. I found jquantlib and quantlib (C++). Any other recommendations? The jquantlib site seems to be down. I'd prefer ...
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Analysis of Unbalanced Covered Calls

Hello I am doing an analysis on covered calls with and extra amount of naked calls. Ignore the symbol and current macroeconomic events. I couldn't find any reference to this strategy (unbalanced is ...
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Early exercise of American options

I know this question is considered basic and has been asked millions of times, but I have done my research and there are some points that I just can't understand. For an American call, many ...
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Are bid-ask spreads in options related to bid-ask spreads in their underlying?

If an underlying has a large bid-ask spread, does it mean that its options will have large bid-ask spreads too? Is there any relation between the bid-ask spreads of options and the bid-ask spreads of ...
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Why does borrowability of shares inversely correlate with probability of assignment or exercise?

I transcribe 5:26 of this video. I don't know that YouTuber's credentials. So looking back here, what could possibly cause you to get assigned early? If we look right here, AMD shares are listed as ...
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Risk-Neutrality: Discount factors of the $P$ world according to risk preferences?

I am coming to terms with the connections between the so-called $P$ world and the $Q$ world. In my understanding, the risk-neutral measure $Q$ induces a probability space under which investors are ...

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