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.

389 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
1
vote
0answers
47 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 ...
1
vote
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 ...
1
vote
0answers
66 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 ...
1
vote
0answers
54 views

characteristic function - fourier pricing

Some literature states that, for instance for the Heston model, the characteristic function is given by: $$\varphi_{\mathrm{H}}(u, t, T)=\exp \left(A(u, t, T)+B(u, t, T) V(t)+i u X(t)\right)$$ Other ...
1
vote
0answers
44 views

What are your favourite papers about European/American options?

I'm looking for some papers to support some options lessons for non-quant people (mostly traders) and I'd like to know what papers would you recomend that don't have a very strong focus on the ...
1
vote
0answers
30 views

Replication Portfolios and Binomial Option Pricing

To price a call/put option with two possible future states of the world, I understand we can price the option by essentially calculating the price of a replicating portfolio that gives the same ...
1
vote
0answers
33 views

Fourier transform of price function

If the expiry value is given by $f(x,T) = e^{-c x}$ for $x \ge a$ and 0 otherwise and c is a +ve constant, prove that in the Fourier domain: $$ (c + j \omega) F(\omega, 0) = e^{-rT} e^{-a(c+j\omega)}...
1
vote
1answer
38 views

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 ...
1
vote
1answer
129 views

Expected Delta hedging frequency as function of implied (and realized) volatility

I'm looking for a proxy (or some rule of thumb) that can create a link between the implied volatility, the realized volatility and the frequency of Delta hedging required to keep the Delta as close as ...
1
vote
0answers
18 views

CVA for a portfolio of long and short options

I am looking to estimate the CVA/DVA for a portfolio of options. For simplicity sake, let's assume there are two FX options in the portfolio, one long and one short. Both options have the same ...
1
vote
0answers
71 views

Trading options - real life vs. textbook?

I'm a Management with Finance student and we have recently learned about options. Because I find it easier to learn these things when I have some context to apply them to, I put $100 in my brokerage ...
1
vote
0answers
41 views

Understanding Options strategies pros and cons

I have been trying to understand options and how to choose Strike prices and Expiration dates as well as the greeks, but I'm not sure I get it. I've ignored volatility or vega for now. From what I've ...
1
vote
0answers
84 views

Attributing hedging p&l to several options

Given a delta-neutral portfolio of one underlying stock and several options, I'm trying to attribute stock trading p&l to the options (assuming the underlying is traded only for hedging purposes)....
1
vote
0answers
66 views

Some basics of option pricing

I am a mathematician trying to learn finance on my own. Try to avoid financial lingo in your answer when not necessary. So I am trying to understand (European) option pricing under the no free lunch ...
1
vote
1answer
105 views

What is the probability of a lookback option ending in the money (CRR-model)

I would like to compute the probability that a certain lookback option ends in the money, let's say that the option has the following payoff $h_N=\max\left\{0,K-\min\{S_1,...,S_N\}\right\} $ where $K$ ...
1
vote
0answers
57 views

Vol surface fitting with 5 degrees of freedom

For an options market making operation I need to be able to build a volatility surface, based on only 5 degrees of freedom, like e.g.: MaxPut, MaxCall, Skew, Curve and At The Money Vol. Is there an ...
1
vote
0answers
78 views

How to price a put option on a multi-asset fund? Confused by risk-neutral pricing implicaton on real world

The fund has super track record with stable vol. The chance for this Put to pay out is very low in real world, but a B/S risk-neutral pricing would give a very high cost. I am struggling with the ...
1
vote
0answers
37 views

Selecting strike prices for put-writing strategy based on Z-scores

I'm trying to replicate the put-writing strategy of Jurek and Stafford from 2015 (The Cost of Capital for Alternative Investments, Jrl. Fin. SSRN). Their strategy writes index put options on the SP500,...
1
vote
0answers
50 views

Practical approach to get average option IV

Is there a practical method to calculate some sort of average IV for each level of moneyness of equity options? I'm thinking of an algorithm to find mispriced options and do to so, we need to figure ...
1
vote
0answers
87 views

Risk-neutral price of $H=e^{X_T^1+X_T^3}$

Let $B=(B_t^1,B_t^2,B_t^3)$ a $\mathbb R^3$-valued Brownian motion. Let $r_t$ (risk free rate) be bounded and deterministic. Let consider the DISCOUNTED market $$d\overline X_t^1=\frac52dt+2dB_t^1-...
1
vote
0answers
65 views

Calculate upper bound for put option prices?

I need to know historical option prices for backtesting. The problem is I don't have such historical data. Is there a way to calculate the upper bound for out of money (American) put option selling ...
1
vote
0answers
34 views

What is the effect of put call open Interest on price action

how option put call open Interest affects price actions as put sellers feel price when price goes down or call sellers feel pain when price goes up and how this affects price action. ie when price ...
1
vote
0answers
53 views

Relationship between Calendar Spread Arbitrage and Probability Density Function (pdf)

We all know that the butterfly spread no-arbitrage condition can be expressed as an inequality restriction on the second-order derivative $\partial ^2C/\partial K^2 \geq 0$, which also means the ...
1
vote
0answers
65 views

Proving an Expectation

Assume the risk-free bond $B_t$ and the stock $S_t$ follow the dynamics of the Black & Scholes model without dividends. Consider the perpetual American put option with payoff $(K-S_\tau)^+$ when ...
1
vote
0answers
26 views

Option Bounds in a risk-averse incomplete market

I was reading the article "On option pricing bounds" by Ritchken(1985). It uses linear programming to determine options upper and lower bounds. Given a single period model, the stock price will have ...
1
vote
0answers
48 views

Equity option demand and supply

Some academic studies have documented that market makers short index option and long equity option on net. It is easy to understand that Non market makers want to buy index option because of their ...
1
vote
0answers
43 views

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 $...
1
vote
0answers
57 views

Log Contracts on Equities

Are log contracts on (e.g) equities traded a lot in the market? I have seen that a lot of it is described for volatility modelling in bergomi's book. what is the liquidity of such options?
1
vote
0answers
66 views

Pricing exchange options

I am really puzzled about the mechanism of pricing of exchange options using a change in numeraire: Suppose that $S^{(1)}$ and $S^{(2)}$ are stocks satisfying SDEs $$dS^{(1)}_t = \mu_1 S^{(1)}_t \,...
1
vote
0answers
53 views

How To Calculate The Implied One Day Expected Return For Earnings

I am trying to figure out how to calculate the one day expected return given I have the event volatility. In his book Trading Volatility, Correlation, Term Structure and Skew, Collin Bennet (link) ...
1
vote
0answers
35 views

relationship between option vol and option payoff

Has anyone thought of the relationship between the option vol and distribution of option payoff? for example, I have 1000 paths of simulated underlying prices, keeping all inputs the same but only ...
1
vote
0answers
64 views

What is the name of these digital basket options?

Consider a basket of correlated assets $(S_1(t),\ldots, S_N(t))$, as well as a vector of strike prices $(K_1,\ldots,K_N)$, and let's look at the following European payoff types: An option that pays 1€...
1
vote
0answers
58 views

Procedure of model calibration

Say that your end goal is to price an equity exotic derivative under both Heston and the local volatility models (Black Scholes model with vola dependent on strike and underlying level). Do the ...
1
vote
0answers
110 views

Optimal Hedging of Options - asymmetry between long and short vol positions

Going over Zakamouline's Approximation method for optimal delta hedging of options, it is claimed that the result remains valid for both buying options (long vol positions) or selling options (short ...
1
vote
0answers
74 views

Numerical Solutions to PDEs with Financial Applications

I am reading a paper by Richard White, Opengamma named Numerical Solutions to PDEs with Financial Applications. There is an implementation codes as stated in paper hosted at https://opengamma.com/...
1
vote
0answers
78 views

option model value vs market price

In my job as FX trader we use as option pricer a variant of B&S. We use that model for “accounting” purpose, i.e. for storing the daily P&L of the portfolio, and also for control the trading ...
1
vote
0answers
40 views

Price moneyness vs spread moneyness for credit index options (CDX HY)

Is spread moneyness equivalent to price moneyness for volatility surfaces of CDX HY? In other words, is the ISDA converter a linear transformation? I have market data that I need to convert to input ...
1
vote
0answers
129 views

Black-Scholes vs Blacks model. Which one to use with SABR?

Say I want to compute a call price for a given set of SABR parameters. I use Hagans approximation and compute $\sigma_B$. The rate is not zero. Should I then compute the option price using Blacks ...
1
vote
0answers
99 views

Generalisation of calendar arbitrage condition to options on futures

This question has discussed the condition on which calendar arbitrage opportunities arise for European call options on a stock. Do similar criteria exist for European options on futures? The most ...
1
vote
0answers
55 views

Spread vol for interest rate spread options in normal environment

Suppose I am long spread option with underlying : rate A - rate B. The vega on the option would be positive. But if I want to compute the option vega with respect to individual rates, can I use the ...
1
vote
0answers
87 views

What is the cause of a “broken” volatility surface?

I am currently working on a project for which I need the implied volatility surfaces, to estimate the value of plain-vanilla European options with different strikes (cannot be observed directly in the ...
1
vote
0answers
32 views

Why do simulation schemes have difficulty in pricing options with low spots?

If you apply a simulation Scheme (log-Euler discretization, Euler discretization and even more advanced ones) on for instance SABR and other models, then they price a call option (where we can easy ...
1
vote
0answers
79 views

Credit spread model

Let $c(t,T):=-\frac{1}{T-t}[\mathrm{ln}(P_1(t,T))-\mathrm{ln}(P_0(t,T))]$, with: $c$ measure of how a company is prone to fail; $P_0(t,T):=e^{-r(T-t)}$ price of no-defaultable bond. $P_1(t,T):=\...
1
vote
0answers
54 views

Books and techniques to hedge options that expire tomorrow?

Can anyone point me to books or resources that talk about best techniques to hedge ATM or close to ATM options that expire tomorrow. I am particularly interested on how to hedge if you are short the ...
1
vote
0answers
27 views

Pricing barrier option under Levy process: Biased estimate?

I want to price a down and out call, barrier option, with the underlying asset following a Levy process. I am interest on the Kou double exponential model or the NIG process, to capture asymmetric ...
1
vote
0answers
47 views

Why can't we create a “magic” basket of options to sell for no-arbitrage pricing in SVJ model?

I am learning how to price SVJ options and am reading some stuff on no-arbitrage pricing for SVJ model using the typical approach you would use (like in BSM option pricing) of creating a risk free ...
1
vote
0answers
62 views

How would one go about pricing a FX future?

What model/equations would I require to calculate the price for a foreign exchange future? This is in an attempt to mitigate foreign exchange risk. Also, how could one measure a business's exposure to ...
1
vote
0answers
94 views

Valuation of Callable Bonds

Is there any way to price American Callable Bonds (those which can be called on any date before expiration) other than basic CRR interest rate trees, since they won't be accurate enough to give ...
1
vote
0answers
48 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 ...
1
vote
0answers
67 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 ...

1 2 3
4
5
8