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.
1,408
questions
2
votes
1answer
55 views
Problem of stochastic differential equation (SDE)
Please help to answer this stochastic differential equation (SDE). Thank you very much.
2
votes
0answers
18 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
137 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
13 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
29 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?
4
votes
1answer
217 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
118 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 ...
8
votes
2answers
3k views
Pricing of a Foreign Exchange Vanilla Option
To understand how Bloomberg prices foreign exchange vanilla options , I extract the following screenshot from its OVML function.
The Black-Scholes formua for vanilla options are
\begin{split}
& P=...
9
votes
5answers
28k views
Why do some people claim the delta of an ATM call option is 0.5?
I am looking for a mathematical proof in terms of differentiating the BS equation to calculate Delta and then prove it that ATM delta is equal to 0.5.
I have seen many books quoting delta of ATM call ...
2
votes
0answers
24 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
47 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 ...
1
vote
1answer
33 views
some questions about pricing an asset or nothing put option with a strike price equal to St
I am working on a homework exercise where the aim is to price an asset or nothing put with K = St, offcourse the normal formula could be used St * N(-d1), but I was wondering if pricing the asset by ...
1
vote
0answers
50 views
FX option trading [duplicate]
Are all trades quoted in implied vol terms delta neutral trades?
If trades are not delta neutral at the initiation does that mean it is speculative trading? Why/ why not?
4
votes
1answer
194 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 &...
0
votes
0answers
44 views
Strictly increasing asset price under a risk-neutral probability measure?
I am reading a paper on option pricing under jump processes in continuous time. There is a section labeled examples where the authors work under a risk neutral probability measure and derive option ...
2
votes
0answers
50 views
Pricing of future options
I have the following question on futures options:
There is a Black’s model, which is a variant of the Black-Scholes formula that is used to price stock options. The Black’s model prices future ...
2
votes
0answers
58 views
Understanding the notion of future options
I am currently studying different types of option-related derivatives and I am quite confused about the notion of “futures options”.
My textbook says that
A futures option is the right, but not ...
2
votes
1answer
99 views
Selling an option before maturity
There is one problem that bothers me:
Let’s say I buy a European put option with a certain maturity date with premium \$1.6 Suppose that the market price of the put option rises before maturity (\$3) ...
2
votes
0answers
33 views
Stratified sampling in asian options
I am using the procedure of stratified sampling for variance reduction. In the Glasserman book the algorithm for stratified the terminal value of the Brownian motion is given for european options. For ...
1
vote
0answers
48 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
1answer
55 views
Intuitive explanation of why ITM options have low Time/Extrinsic Values?
While brushing up on my knowledge about the Greeks, I have been struggling coming up with an intuitive, probability-based explanation behind why not only Out-of-the-Money (OTM), but also In-the-Money (...
0
votes
1answer
31 views
Relationship between portfolios at $t=0$ based on $t=T$
I have two portfolios $V$ and $U$ given by
$$
V(S,t) = C-P \\
U(S,t) = S-Ee^{r(t-T)} \\
$$
where $P$ and $C$ denote a put and call option with the same maturity time $T$ and strike price $E$, ...
4
votes
1answer
74 views
Option pricing: Relationship between Theta and early exercise
I am confused about the following:
For a European put option, the parameter $\Theta$ is given by
$$ \Theta= \frac{d V}{dt} = -\frac{SN'(d_1) \sigma}{2 \sqrt{T-t}} + rK e^{-r(T-t)}N(-d_2).$$
My ...
4
votes
3answers
1k views
Effect of interest rate on options prices
This might be another basic derivatives question. When interest rate rises, stock prices generally fall. Assuming an option's underlying is a stock, this should lower the option's price as well. ...
0
votes
1answer
51 views
Why Joshi defined option value to be discounted payoff using risk neutral expectation?
Currently I am reading Mark Joshi's The Concepts and Practice of Mathematical Finance.
At page $59,$ the author mentioned the following.
Instead
of requiring that every portfolio should have ...
1
vote
1answer
37 views
Historical quotes / prices of multiasset options
I am working on Lévy copulas, and I would like to try calibrating such techniques on real data. Where can I find quotes for multi-asset options? It could be exchange options or any other type of ...
0
votes
1answer
32 views
Are the price of vanilla bull/bear spread constructed by calls and puts same?
We know that both bull and bear can be constructed by either two calls or two puts. Say if given two strikes, will price of bull call equal to price of bull put?
1
vote
0answers
36 views
What is the name (Greek) for sensitivity of an option's Theta to the Time to maturity?
All other second order sensitivities of option prices to underlying price, volatility and time, seem to have a commonly accepted names: Gamma, Vanna, Charm, Vomma/Volga, Veta as documented here (...
1
vote
0answers
32 views
What are popular metrics for Option Skew?
What are popular metrics to track skew? Would it be the difference between OTM option and ATM option IV? Would it be a percentage difference in IV?
Also, if both are valid, would a % change be ...
3
votes
0answers
56 views
How to shock the IV surface w.r.t VIX and keep AOA
I have to compute the sensitivity of a set of option prices on a single sotck (range of tenor is over the whole surface) to an increase of 100% in the VIX.. and I am trying to get to the most ...
2
votes
0answers
38 views
what is the state of the art method for hedging barrier options?
I want to create my own Barrier options for some security, I want to trade. I did some literature review, and found a static replication method, and many dynamic replication methods. I want to know ...
0
votes
0answers
36 views
Option arbitrage on two correlated or cointegrated underlying assets
If two indices are highly cointegrated, does it allow for some set of statistical arbitrage strategies for european options for which those indices are single underlyings ?
Does answer change if ...
11
votes
3answers
4k views
Carr-Madan Formula
Really new to financial Maths. I am currently having problems with the Carr-Madan Formula.
$$f(S_T)=f(F_t) + f'(F_t) (S_T - F_t) + \int_0^{F_t} f''(K) (K-S_T)^+ \ d K + \int_{F_t}^{\infty} f''(K)...
2
votes
1answer
59 views
Arbitrage-free IV surface definition vs. real arbitrage process
In the context of BS implied volatility surface fitting.
In the literature, it seems that conditions for arbitrage are defined in a way that assumes that options can be traded at the same price for ...
4
votes
1answer
2k views
Option prices in Bates SVJ model?
In this [post] discussed the European put and call price formulas under the Heston Stochastic Volatility model.
There exists an important extension of Heston model to include diffusion jumps, known ...
2
votes
2answers
101 views
How to derive Black-Scholes equation with dividend?
Question: The Black-Scholes equation without dividend is given by
$$\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2S^2\frac{\partial^2 V}{\partial S^2} + rS \frac{\partial V}{\partial S} -rV = ...
1
vote
0answers
38 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) ...
0
votes
0answers
35 views
Is my derivation of Black-Scholes equation correct or am I missing something (eg assumption)?
Question: The following is my derivation of the Black-Scholes equation. Is it correct or am I missing some details (eg assumption)?
Let $V$ be value of an option.
Suppose value $\Pi$ of a portfolio ...
3
votes
3answers
129 views
Explain that gamma is positive for standard call and put options without using heavy mathematics
Gamma is positive for any standard put and call options seems like a standard fact.
A proof can be found in this post.
However, the answer provided in that post involves heavy mathematics.
Is ...
5
votes
1answer
406 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 ...
2
votes
1answer
42 views
Compute Vega and Delta in R
I am trying to compute greeks for a large sample of CEO compensation contracts in R. However, my vega computations all result in a value of zero.
In doing so, I follow Core and Guay [2002]:
Here is ...
3
votes
1answer
38 views
Show that $\frac{\partial c(t))}{\partial \sigma^2 }>0 \text{ if and only if } S(t)<Xe^{-r(r+\frac{1}{2} \sigma^2 )(T-t)}.$
Statement: if $c(t)$ is the price of the digital cash-or-nothing call option, then direct calculation (under Black-Scholes assumptions) shows that
$$\frac{\partial c(t))}{\partial \sigma^2 }>0 ...
-2
votes
1answer
46 views
HEDGING WITH A PUT OPTION
In the following example, for 3rd question and 4th question why do we have to add (Stock price in three months - Current stock price) to put option profit?
Thank you in advance.
1
vote
0answers
29 views
How to adjust delta hedging if stock price decreases?
Question: You are long a call option no MITCO stock. You have delta hedged your position. You hear on the radio that the CEO of MITCO has just been arrested for running a massive Ponzi scheme. The ...
0
votes
0answers
14 views
Applications of a calibrated price or IV surface and other basic questions
Newbie here with basic questions. I have researched the topic online, but am still at a loss. I went through a nice course on calibration, saw how to apply stochastic short rate, stochastic vol, jump ...
1
vote
1answer
42 views
Do not understand 'The gain (loss) on the stock position would then tend to offset the loss (gain) on the option position' [closed]
Currently, I am reading John Hull's Options, Futures and Other Derivatives. On page 401, the author mentions the following:
Suppose that the delta of a call option on a stock is $0.6$, stock price ...
1
vote
1answer
73 views
Duan (1995) GARCH Option Pricing Model with MATLAB
This is the MATLAB code that replicates the option pricing model proposed by Duan in his paper "The GARCH Option Pricing Model". However, the parameters estimated in the file do not match with the ...
1
vote
1answer
55 views
If the volatility is zero (i.e. σ=0), what is the call worth? After valuing the call, how to hedge the call (assuming you sold it)
Question: All Black-Scholes assumptions hold. Assume no dividends. The stock price is $100. The riskless interest rate is 5% per annum. Consider a one-year European call option struck at-the-money (i....
0
votes
0answers
16 views
American Option - Early exercise risk management
This is for American Option Book Management in real trading.
Let`s suppose,
American Option seller(Book manager) only do delta hedging, which means seller cannot do Vega hedging,
American Option ...
4
votes
1answer
108 views
Implied interest rate using put-call parity
In the process of asking this question, I acutally found the solution. I still let this post open if it can be interesting to someone else and have added a related question at the end.
I want to ...
