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.

Filter by
Sorted by
Tagged with
1
vote
1answer
20 views

Arbitrage opportunity between two call options with strike price \$40, \$30 and cost \$4, \$3 respectively?

Question: Given two call options $c_1$ and $c_2$ with strike price $30$ and $40$ respectively. If $c_1$ costs \$3 and $c_2$ costs \$4, is there an arbitrage opportunity? My attempt: Short $c_2$ and ...
-1
votes
1answer
33 views

Graph of European call option value versus future price

Given a standard European call option on a non-dividend-paying stock. Draw the graph of call price at time $t$ versus the future price $F(t,T)$. The future price $F(t,T)$ is observed at time $t$, ...
0
votes
1answer
43 views

Delta of an option which is approaching expiration when stock price decreases

The following is an interview question. It is 10 months since you sold a one-year European call option to a customer. You have been delta-hedging your exposure to the written call since it was sold....
0
votes
2answers
67 views

Why are put and call options worth the same despite that put has no upside whereas call has unlimited upsides?

The following is an interview question. All Black-Scholes assumptions hold. Assume no dividends. Consider a standard European call and a standard European put on the same stock. Assume that each ...
2
votes
1answer
78 views

Hull-White calibration volatility as a function of time

I need some help for the parametrization of the volatility parameter in the Hull-White model. I have the necessary Caplet vols and I calibrated the HW model to match the Caplet and hence the Cap ...
1
vote
1answer
64 views

Hedging delta when gamma is positive

If I have an aggregate position with a positive gamma, should I still be delta neutral? I feel like I'm giving up the positive benefits of being gamma positive because I'm killing my delta constantly.
0
votes
1answer
35 views

Calibrating Heston model parameters using the Active-set method and Levenberg–Marquardt

Background: We're estimating the parameters of the Heston model from current market data of options. This is to be implemented using the active-set method (see section 16.5 here) and the Levenberg-...
1
vote
1answer
56 views

How does longer time to maturity affect standard European call and put option values?

Denote American call and put option values as $C$ and $P$ respectively. Similarly, denote European call and put options values as $c$ and $p$. It is well known that time to maturity affects all $C,P,...
1
vote
2answers
67 views

Future Volatility Trading

I want to find a way to long volatility of a future time period such as longing (march,april) vol from today. My idea is to short a straddle for march and long one for April for example. Will that ...
4
votes
1answer
157 views

What does is mean by buy(long) volatility or sell(short) volatility in option trading specifically?

I often hear this term quite lot from traders, what does it really mean? And some additional question: In option trading, is "buying vol" equivalent to "buying option" (no matter it's call, put or ...
0
votes
1answer
89 views

Pricing European call with Feynman-Kac

I am trying to calculate the solution to the Black-Scholes (BS) equation using the Feynman-Kac (FK) formula for a simple European call. According to FK, the solution to BS is the discounted average of ...
1
vote
3answers
67 views

Calculate uncertainty of option expiring ITM

I know it is pretty straightforward to determine the probability that an option will expire OTM -- basically a 0.10 delta call will have a 10% probability of being ITM at expiration (see this question)...
0
votes
0answers
54 views

Testing Option Strategy

I have a long only momentum system that has back tested well and live results have been ok. I would like to see if I can use these signals to sell Puts to see if it improves results. Not looking for ...
0
votes
0answers
41 views

Modelling Theoretical Value [closed]

Quick bit of background. I'm adding a little options market making into my normal crypto derivatives trading, and I'm currently writing the software to help me do that effectively. One thing I'm ...
2
votes
0answers
47 views

Leverage of various option types

Does the standard European option calculation of leverage, Embedded Leverage = Delta times (Underlying price/Option price) change across the various option ...
-2
votes
1answer
120 views

Specific Hedge Fund Filed Returns

https://mebfaber.com/2008/12/27/tracking-jim-simons-renaissance-technologies/ But, like always, I will let the data speak for itself. Top 10 holdings, back to 2000, equal weighted through 12/19/2008:...
2
votes
1answer
96 views

Effective gamma/vega hedging

I want an options position where I can short some options to pocket the premiums and benefit from the time decay. I also want to be vega and gamma neutral. Is there an established way to find which ...
0
votes
0answers
44 views

How to hedge payments in a foreign currency?

I´m confronted with solving the following exercise: "Suppose that now is 1 March. You are a UK based exporter who´ll export products to a U.S. company for 250,000 US dollars and to a French company ...
2
votes
1answer
92 views

How many options would be required to dynamically replicate the VIX nowadays?

The VIX is a portfolio of OTM options on the SPX with non-zero quotes. From CBOE white-paper: Only SPX options quoted with non-zero bid prices are used in the VIX Index calculation. [...] As ...
0
votes
1answer
61 views

Cox-Ingersoll-Ross Zero Bond Put Option

according to Brigo & Mercurio (2006): But how is the Zero bond Put of the CIR model? I couldn't find any information about that. Thanks in advance. Regards Chris
4
votes
2answers
162 views

Deriving implied volatility programmatically

I'm working on a project to calculate the value of options using Python. I'm using the Black-Scholes model, and I can get accurate results by plugging in a given ...
0
votes
0answers
22 views

0 Delta on Forward starting Equity basket option

I wanted to confirm the inherent reasoning behind 0 delta on a weighted equity basket option. For instance, if we have a basket option with a forward starting initial fixing date, we can expect the ...
5
votes
2answers
473 views

Numeric example to understand the effect of option gamma

Gamma of an option is the second partial derivative of the theoretical value of an option wrt the underlying. It should be the rate of change of Delta wrt to a small change on the underlying. However ...
1
vote
1answer
57 views

Variance of a spread for options on spreads

I was reading the paper: https://people.umass.edu/nkapadia/docs/Negative_Vega.pdf In the equation $(5)$, he is defining the variance of the spread as: $$\sigma_1^2S_1^2 + \sigma_2^2S_2^2 - 2\...
0
votes
0answers
39 views

Hedging option delta

Let's say I am long 1000 50 delta call options. I need to hedge my deltas now. There can be infinite ways to do this. How should I think about proceeding wit this? My first thought was, if the ...
1
vote
0answers
62 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 ...
0
votes
2answers
112 views

Proving a process is martingale under the Risk Neutral Measure

Show that for any $\lambda \in \Re$, the process $Y_{\lambda,t}$ defined as: $$Y_{\lambda,t} = (S_t/S_0)^\lambda e^{-(r\lambda-\lambda(1-\lambda)\sigma^2/2)t}$$ is a martingale under the risk ...
2
votes
1answer
45 views

theta for SPX options vs. E-mini future options

Interactive Brokers currently shows the following data for SPX options at strike 3000 and expiry 2020-09-17: calls: bid/ask 234.10/236.30, theta -0.362 puts: bid/ask 146.70/148.40, theta -0.225 Then ...
2
votes
1answer
147 views

Floating Strike Lookback Call Option

Assume the risk-free bond $B_t$ and the stock $S_t$ follow the dynamics of the Black & Scholes model without dividends (with interest rate $r$, stock drift $\mu$ and volatility $\sigma$). If $r=\...
4
votes
2answers
519 views

Finding price of the power option

Let's assume a market with $d=1$ and $X=X^1$ satisfying $dX_t=\sigma X_t\,dW_t,\: \: X_0=1,$ where $(W_t)$ is a standard Brownian motion. Assume that $\mathbb{F}$ is the natural filtration of $X$ ...
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
2answers
90 views

Instantaneous change in value of portfolio

I am trying to figure out an intuitive explanation for the instantaneous change for the value of a portfolio (essentially I'm creating a self-financing portfolio to replicate a derivative payoff). ...
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 ...
0
votes
0answers
51 views

construction of 25 delta butterfly

Could anyone explain why the 25-delta butterfly strategy is constructed by 0.5*(25-delta call + 25-delta put) - ATM straddle? Especially, what the term "25-delta" represents in "25-delta butterfly ...
1
vote
0answers
49 views

Why does the price of a butterfly spread increase are rate exponential [closed]

I know that stock prices are assumed to be Stochastic processes that follow Geometric brownian motion. The expectation of stock prices at time T given stock price at time 0 is: $e^{-rT}S_0$. However, ...
4
votes
2answers
277 views

Best topics to begin Quantitative Finance Research/Programming

I have a background in mathematics (Functional Analysis and Probability Theory) and am looking to acquaint myself with research in quantitative finance, particularly with a programming component. ...
2
votes
0answers
39 views

Replicating portfolio with stock, bond and call option

I am trying to interpret: I am having trouble interpreting the replicating strategy: Context: $\phi$ is a generic payoff function, 0 < S < $\infty$, assumed throughout to be twice ...
1
vote
0answers
28 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 $...
2
votes
1answer
80 views

Are vega vanna volga methods/models used in equity derivatives or only in FX and why?

Vega vanna volga models seem to be popular is the FX derivatives market and are often calibrated via 25 delta risk reversal, vega weighted butterfly, and ATM straddle quotes. I am wondering if they ...
1
vote
1answer
72 views

Which currency to hedge a position in FX options?

Let's assume a bank sells to a client a put of \$1,000,000 dollars on USDJPY at 110 in 6 months. The delta of this put is -0.6, spot is 112. So to hedge its position the bank has to short \$600,000 ...
0
votes
0answers
27 views

Reading this ichimoku cloud how do you read this wdfc chart?

Having trouble reading the charts as the breakouts aren’t clear What do you see in this chart?
2
votes
0answers
22 views

Data sources for historical ICE settlement option prices, volume & open interest

I am looking for long history for historical settlement option prices, volume & open interest at ICE Europe (specifically fixed income). This seems to be more challenge than I could imagine. ICE ...
2
votes
1answer
162 views

For which would you expect the liquidity on instrument X to be the greatest: its spot, future, option or swap?

Would like $X$ to remain general, but if needed, let's say GBPUSD Exchange Rate. By liquidity I mean overal market volume across exchanges / ease of opening and closing positions / total notional ...
2
votes
0answers
20 views

Implying a required rate of return on an option from the required rate of return on the underlying

Is it possible to imply a required rate of return on an option from a required rate of return on the underlying? For example, given a known cost of equity, can you calculate the required rate of ...
1
vote
0answers
36 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?
2
votes
1answer
113 views

Problem of stochastic differential equation (SDE)

Please help to answer this stochastic differential equation (SDE). Thank you very much.
4
votes
1answer
253 views

Options basics needs to be cleared

I'm not clear for the terminology of options and the mechanics of it. Any help is appreciated. For example the following statement: European call option of Apple stock with maturity 1 year and ...
4
votes
1answer
167 views

Why do options market makers make their spread as wide as the corresponding vega?

I've heard that option market makers make their bid ask spread as wide as the vega of the contract they are quoting. If the quoted spread is narrower than the vega of the option it is said that the ...
2
votes
0answers
32 views

CVA for options

I am trying to do a simple unilateral CVA for call and put options. I found this discretised formula online: $$ CVA = \sum_{i=1}^m \frac{EE(t_{i-1})DF(t_{i-1}) + EE(t_i)DF(t_i)}{2} \left( PD(t_i) - PD(...
2
votes
0answers
52 views

Delta Hedging Example

I was reading Dynamic Hedging by N. Taleb and in the chapter dedicated to the delta, there is this example of a trader position in options (one-month European call, flat yield curve, forward is ...