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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2
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0answers
8 views

how we can derive $PIDE$ of double exponential Jump-diffusion model (we know as kou model)?

I'm working in double exponential Jump-diffusion model (we know as kou model) with following form , under the physical probability measure $P$: \begin{equation} ‎\frac{ds(t)}{s(t-)}=\mu‎‏ ‎dt+\sigma ...
3
votes
1answer
15 views

Forced to exercise gap options

I was reading a textbook and came across some surprising stuff in the section about gap options. Let $X$ be a payoff function such that $X=\Big\{\matrix{0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...
3
votes
2answers
32 views

Implied volatility and nonconstant volatility

John Hull states in his text that "AS the maturity of the option is increases the percentage impact of nonconstant volatility on (option) prices becomes more pronounced, but its percentage impact on ...
2
votes
1answer
43 views

VaR calculation methods of options

I am a little bit confused about VaR in Options and I need a clarification for. I collected the following formulas, can you suggest what is the best formula and explain me why, please?
1
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0answers
17 views

In this scenario could gamma be higher for OTM options?

Let's say there is a $1 stock, with say 1 day to expiration. The 1.5 strike call, is probably a 0 delta at this point; however, a 1 point increase would mean the stock would be at trading at 2 ...
3
votes
1answer
153 views

Closed form solution of PDE of Option Price

Let $V=V(S_t,t)$ be the option price and \begin{align} V_t+\mu\,S\,V_S+\frac{1}{2}\sigma^2\,S^2\,V_{SS}=0\\ V(S_T,T)=\ln (S_T)^{2}. \end{align} My question: How can I obtain a closed form solution of ...
3
votes
2answers
62 views

Do futures follow physical or risk-neutral distributions

I've spent a while looking for an answer to this question and while I feel it is a simple question I have not found an answer. I know prices of option contracts follow an implied, risk-neutral ...
4
votes
1answer
29 views

Boundary Condition for Convertible Bond under Two-factor Model Interest Rate

I want to find Boundary conditions for Convertible Bond under Two-factor Model Interest Rate.The portfolio contains stock where stochastic differential equation for the stock price is \begin{align} ...
4
votes
2answers
159 views

good R package for vectorized option pricing

I am using for now the package fOptions but it doesn't allow for vectorized computation of black76 prices and delta. Which package can be used to do that? As noted ...
3
votes
1answer
35 views

Why risk-free interest is needed for Margrabe's Formula?

The source code for Margarble's formula in QuantLib is here. The implementation requires a forward price be computed: ...
4
votes
1answer
62 views

Numerical example of how to calculate local vol surface from IV surface

I'm looking for an excel example (not a copy of Dupire's eqn) of how to convert an IV surface to a local vol surface. If unsuccessful I'll work through Dupire's eqn but would be helpful to look at an ...
2
votes
1answer
45 views

Why can't you arb skew by buying options with low implied vol and selling high implied vol in the same month and dynamically hedging?

there's something I've been trying to understand for a while now and I just can't quite understand with regards to skew. In the same month, why can't you buy a option that have low implied vol on the ...
2
votes
1answer
89 views

Boundary conditions of PDE from SV model with stochastic interest rate

The PDE for the American put option price $P(S,\sigma ,r,t)$ is \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + ...
0
votes
1answer
63 views

Local volatility parametrization using the spot

Is it possible to estimate the local volatility using the spot price S at time t instead of the strike price K and the expiry date T ? Any help would be appreciated.
1
vote
2answers
73 views

Hedging portfolio and extraction PDE of SV model with stochastic interest rate

How can I extraction this PDE \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + \frac{1}{2}P_{\sigma ...
2
votes
1answer
61 views

Options on Volatility Control Index

I have two question. Does an option on volatility control index exist? If I google it, it seems like there is such an option, but I can't find the option on any of exchanges. So this is my first ...
0
votes
0answers
21 views

Intermediate Project Presentation

I would like to know an ideal plan for explaining/representing Greeks (1st,2nd,3rd) order. The topic seems to be quite vast and very interesting but not possible to cover within a 15 mins time frame, ...
1
vote
0answers
50 views

Price of an American call option [closed]

I'm working through revision questions at the moment and we are asked to compute the price of an American call option. Suppose that $dS_t = \sigma S_t dW^*_t, S_0 >0$ Let $0<U<T$ be fixed ...
2
votes
1answer
98 views

How to hedge a put under the Black-Scholes model?

To hedge a call, one would invest the option price proceeds into $\Delta_t*S_t + B_t = c_t$. (ok) However, a put has negative delta, so I would short $\Delta_t*S_t$ and invest ...
0
votes
0answers
39 views

Benchmarking option pricing under stochastic interest rates

I priced a long-term option (10 or 20 years) using two different models: one assumes constant interest rates, the other assumes stochastic interest rates. Is there a way (e.g. a benchmark) to ...
1
vote
0answers
30 views

replicating strategy three step binomial

I am having some trouble setting up a replicating strategy for a call option with a three step binomial model (discrete). I have no trouble doing this in a two step binomial model by backward ...
0
votes
0answers
40 views

“Hedging” a put option, question on exercise

I have a question on the following exercise from S. Shreve: Stochastic Calculus for Finance, I: Exercise 4.2. In Example 4.2.1, we computed the time-zero value of the American put with strike ...
3
votes
1answer
101 views

Distribution of Black Scholes call option price at time 0<t <T

Does anyone know how to find the probability law (distribution) under P* of a Black Scholes Call Option price $C_t$ for $0 < t < T $? (Under P*, $ dC_t = \frac{\partial c}{\partial s}\sigma S_t ...
1
vote
2answers
159 views

Option arbitrage with dividends?

If a stock pays a discrete dividend, the stock price falls by the amount of the dividend. There is no arbitrage opportunity from this predictable jump, because the investors receive the same amount of ...
2
votes
4answers
193 views

How to short an option?

It appears to me that retail investors can only buy calls and puts, but not short them through any standardized way (except maybe borrowing the option from a friend ;) ). Is that correct, or how can ...
2
votes
1answer
65 views

Transaction costs on option trades

It looks like the commissions alone for a non-index option trade is around 2-5%. For example, a BAC June ATM Call is currently trading at \$0.20; Interactive Brokers charges $0.7 per contract, which ...
5
votes
2answers
89 views

Derivation of Stochastic Vol PDE

A couple questions regarding stochastic vol PDE derivation. Following Gatheral, a general stochastic vol model is given by \begin{align*} dS(t) & = \mu(t) S(t) dt + \sqrt{v(t)}S(t) dW_1, \\ dv(t) ...
2
votes
1answer
74 views

Using FX ATM/RR/BF Volatility to Estimate Smile

Suppose $S$ is some FX rate, EUR/USD say, and $\sigma_{S}(K,T)$ is the implied volatility for some option written on $S$, sourced from the surface $\sigma_{S}(\cdot,\cdot)$ (alternatively, consider ...
5
votes
1answer
123 views

Variance replication using options

I would like to understand the intuition behind the following question: Why a certain weighted sum of prices of put and calls is equivalent to the implied variance of an underlying? A variance swap ...
1
vote
1answer
99 views

Mean reversion time estimation

I am new to mean reversion trading, and I would like to get some good references about how to estimate the time it takes to a mean reverting process to cross its long term mean.
2
votes
1answer
61 views

Black Scholes Model and Dividends

My question can be summarised as such: Consider a portfolio. Say it has a price $\Pi = x$. Portfolio consists of a stock and a sequence of call options underlying on the stock. It has been announced ...
2
votes
1answer
70 views

Black Scholes Formula, drift term

In the formula, the stock return is modelled as a brownian motion that is a drift + a stochastic term, ok I get that. But the drift term is then modelled as r - volatility ^ 2 / 2. I am not sure how ...
6
votes
2answers
165 views

What's the point of discounting in risk-neutral pricing?

Let $\phi$ be a self-financing strategy that replicates a time $T$ option payoff $X$ on stock $S$. By definition of a trading strategy, $\phi$ is previsible. Finally, let $V_t$ be the time $t$ value ...
1
vote
2answers
42 views

Is the Binomial Tree Model not self-financing?

Consider a 2-period binomial tree where the derivative price is $f$ and the stock price is $S$. Also, let the bond be deterministic with continuous growth rate $r$ and initial value $B_0$. binomial ...
4
votes
2answers
91 views

simple, intuitive barrier option derivation

Is there a simple integral that gives barrier option prices without having to deal with messy, hard PDEs and change of variables I understand there is a reflection principle such that the simulation ...
3
votes
1answer
89 views

Why must a replicating portfolio be self-financing?

If I have a trading strategy such that at each time $t$ I own $\Delta_t$ units of stock $S_t$ and $\psi_t$ units of bond $B_t$, it is a replicating strategy for some claim with time $T \geq t$ payoff ...
1
vote
2answers
96 views

Estimate simple option price without a calculator

I have been to two different interviews for jobs related to option trading, and both time I have been asked a question, which is pretty basic, and still I could not answer it. If you have an European ...
-4
votes
1answer
46 views

Can not understand options pricing [closed]

As we are seeing here http://www.theoptionsguide.com/strike-price.aspx Relationship between Strike Price & Call Option Price Relationship between Strike Price & Put Option Price I do not ...
0
votes
1answer
43 views

Negative time value european options

I have a basic question for which I feel like I should have found the answer by googling it, but I didn't get a definitive answer, so here I am: Can the time value for a plain vanilla (European) ...
2
votes
2answers
97 views

Short volatility strategy using strangles

For a short volatility strategy using option strangles, is it better to target a fixed premium to earn? Or a fixed vega? Objective is to maximise the return/risk (sharpe) of the strategy. Any help ...
0
votes
0answers
58 views

Cointegration and variance of time series

Given that $X_t , Y_t$ are two cointegrated random processes, what can we say about the relationship between variance of the two increments $var(X_{t+h}-X_t)$ , $var(Y_{t+h}-Y_t)$ for a given ...
1
vote
0answers
69 views

Black Scholes Model Replicating Strategy Delta Hedged Exam Question

A share is currently priced at 640p. A writer of 100,000 units of a one year European put option with an exercise price of 630p has delta-hedged the option with a portfolio which holds cash and is ...
2
votes
1answer
67 views

Pricing digital options in discrete time

I am stuck in this exercise from my textbook: Consider a one-period market model with $N+1$ assets: a bond, a stock and $N-1$ call options. The prices of the bond are $B_0=1$ and $B_1 = 1+r$, ...
1
vote
2answers
136 views

Intuitive Reasoning for Using Risk-Neutral Measure

Although we thoroughly covered risk-neutral pricing in university I never fully understood it in the context of continuous-time processes. But first of all, lets consider a discrete time example: ...
1
vote
2answers
96 views

Buying OTM puts and then selling stock

What is to stop someone from first buying a bunch of OTM puts and then selling short enough stock to make the puts go up high enough to make a profit? Or conversely, buying OTM calls and then buying a ...
2
votes
0answers
70 views

Modeling market sentiment and pricing options by volume, open interest

Are there any empirically-proven methods/formulas for weighting IV surfaces, pricing a discount/premium in an option, and/or adjusting any of the 1st- or 2nd-order Greeks for the magnitude (volume or ...
2
votes
1answer
54 views

Solving a Non-Linear PDE using a Finite Difference Scheme

I have the following non-linear PDE and I have no idea how to go about solving it using a finite difference scheme in Python. Can someone get me started and/or point me to an algorithm for doing this? ...
0
votes
0answers
53 views

variance ratio for pair-trading

I am using the variance ratio test to check whether my sequence is mean reverting in that test there is a parameter n, How in general I choose this n? or what is the meaning of this parameter? ...
3
votes
1answer
146 views

The meaning of Ornstein-Uhlenbeck parameters

I am trying to understand theOrnstein-Uhlenbeck process $dX_t = \kappa(\theta-X_t)dt + \sigma dW_t$ my question is what is the meaning of the parameters? and assuming that we know those parameters ...
0
votes
0answers
45 views

Binomial function use in Bezier smoothing

I am using the Bezier method to smooth option volatility curves, which utilised the binomial distribution. Is someone able to clearly explain the interpretation of the binomial distribution in the ...