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.

learn more… | top users | synonyms (1)

3
votes
1answer
124 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 $...
3
votes
2answers
147 views

What is the use of options pricing formulas

This may seem like a dumb question, but if the EMH is generally true, wouldn't options already be correctly priced? Why do we need all these intricate formulas, unless we think the prices are wrong or ...
3
votes
1answer
165 views

Different Exercise Style Options on Same Underlying

Some equities on European markets have options traded in two different exercise styles: American and European. Examples: ABB and ABB (european) on Eurex Banco Santander on MEFF Consider ...
3
votes
1answer
342 views

how to define liquidity in equity, index, and etf options

i've heard several ways to put a metric on liquidity of options.. obviously liquidity isn't a constant.. things like the Bid/Asks spread, liquidity of the underlying.. Trying to find a way to ...
3
votes
1answer
568 views

Choice of epsilon for numerical calculation of vega in binomial option pricing model

I have a binomial option-pricing model (I don't think the details of how its implemented are relevant). However, when I go to calculate vega, I am essentially running the model a second time with new ...
3
votes
1answer
443 views

Value options when the currency’s risk free rate is negative?

How would you handle a negative interest rate in index/equity options valuation? An example would be negative rates for short term maturities for Swiss Frank (CHF).
3
votes
2answers
1k views

How to calculate COMPOSITE underlying implied volatility from ATM (near month) option prices?

I am trying to calculate the implied volatility of an underlying given observed prices of call and puts. There are two scenarios: The ATM strike is pinned by the market (i.e. underlying level == ...
3
votes
1answer
117 views

VAR of portfolio containing options, equities and forwards

If we want to calculate VAR of a portfolio using variance covariance matrix (delta normal method), containing equities, forwards and options, how do we treat each asset class for making the variance ...
3
votes
4answers
195 views

Model Price vs Market Price in terms of Fair Price (Options)

Before I start: Ok, this is something I investigated for a fair amount of time and my question is semi-academic. To simplify, I will introduce the short bit (TLDR) of my question and then lay out ...
3
votes
2answers
154 views

American vs European Options on equity index options

I have a question regarding the usage of European vs American Options. According to Professional Risk Mgr Handbook 2010, American-style options are used mostly on equities whereas European-style ...
3
votes
1answer
231 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 ...
3
votes
1answer
114 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 + \frac{1}{2}...
3
votes
1answer
148 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 ...
3
votes
1answer
89 views

Binary option expression

Given r=0, σ(K)=const Binary=lim┬(ε→0)⁡〖((C(K,σ(K))-C(K+ε,σ(K+ε))))/ε〗 What is the analytical expression for the binary option value? σ(K)=const Therefore, Binary=lim┬(ε→0)⁡〖((C(K)-C(K+ε)))/ε〗 ...
3
votes
1answer
196 views

Valuation of Cox-Ross-Rubinstein Model

We have a Cox-Ross-Rubinstein model with parameters $u$ ("up"), $d$ ("down") , $r$ (interest rate) and $q$ (equivalent martingale probability) $(q=(1+r-d)(u-d)^{-1})$ . We have a contingent claim with ...
3
votes
2answers
225 views

stock option strategies long vs short

What makes an option strategy long or short? I got the impression that if it is a net debit (you pay to open the strategy) it is classified 'long' (strangle, straddle) Then I learned about the call ...
3
votes
1answer
275 views

In a covered call strategy, should I hold the call or sell/roll if the delta becomes too small?

I am tweaking a covered call algorithm. The short leg consists of out of the money call options. The goal is to collect the tim premium, but an equally favorable circumstance is when the call ...
3
votes
3answers
158 views

Computing loss of Call / Stock Purchase

A seller of an European Call, can, subjectively have unbounded losses. This loss may be mitigated by buying the stock (covered call). In this case,, the loss will be bounded at A. How would one ...
3
votes
1answer
152 views

Negative adjusted strike in Levy's Asian option approximation?

In Edmond Levy's 1992 paper, he introduced a moment-matching method to approximate the price of an Asian option assuming GBM for the underlying. It suggested that, if some monitor points are already ...
3
votes
1answer
73 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} ...
3
votes
1answer
60 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: ...
3
votes
0answers
106 views

Pre- Versus post-2008 Crisis Rates Modeling

Modeling for interest rate derivatives (such as bermudan swaptions) is said to have undergone significant changes since the crisis. Prior to the crisis, counterparty default risk was often ignored, ...
3
votes
0answers
296 views

Does Bakshi, Kapadia and Madan (2003) VIX building approach underestimate volatility?

From a paper that shortly addresses an alternative approach to VIX-like index building: To test this approach, I've built a fake book of B&S options with constant volatility equal to $\sigma=...
3
votes
0answers
118 views

Estimating risk aversion (power or exponential utility) from options prices

I came across this literature and it seems like there are a number of ways people do this. You can do it for an option on any underlying as long as you can create the risk-neutral p.d.f. If you agree ...
2
votes
6answers
343 views

What is the Benefit of holding a short option?

i am new to corporate finance and ask myself why a investor is interested in being short on a Option? The only he can win is a premium but he can loose much more. I understand with being a short I can ...
2
votes
3answers
1k views

Understanding the concept of Martingale pricing

I am a bit confused about how to formulate a problem where I have to price an option on a stock. Many papers say that stock prices are best modeled using a geometric Brownian motion (GBM), and I ...
2
votes
2answers
50 views

Why would one prefer variance swaps over other instruments?

I understand that an investor who has a view on an underlying's variance would be tempted by a variance swap. But why would one prefer such a contract over another instrument whose value is based on ...
2
votes
4answers
215 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
2answers
242 views

Is it fair to assume $(ud=1)$ in the binomial tree option pricing model?

I have discussion with my colleague on why a general assumption $$ud=1$$ in binomial tree option pricing model would be necessary? I take it a simplification of the problem, otherwise, there will be ...
2
votes
1answer
98 views

Why is $N(d_2)$ not needed for hedging?

I'm trying to understand delta hedging. If I sell a plain vanilla call option, in order to delta hedge it, I have to buy delta amount of stocks. What I don't understand is that the BS price of the ...
2
votes
2answers
277 views

Is implied volatility flawed?

Was going through how Implied Volatility is used by option traders and in delta hedging. Correct me if I am wrong, doesn't IV consider a standard deviation of the stock price over say the past 1 year? ...
2
votes
2answers
1k views

Can we replicate a call option without borrowing and make it cheaper in this way?

I learned how to price a European call option using this video lecture. The considered case is very simple. The call option gives the right to buy 100 Euros for 100 Dollars in one month from now. The ...
2
votes
2answers
113 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
106 views

Boundary Conditions for Call Spread

I was just wondering if someone could verify whether these are the two boundary conditions for a Call Spread Black-Scholes PDE. The first one I have is: $max(S_{T} - K_{1}, 0) - max(S_{T}-K_{2},0)$ ...
2
votes
1answer
232 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
2answers
150 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 ...
2
votes
2answers
91 views

Option pricing, origin of formula $\Pi( t,X)= E^{\mathbb{Q}}\left[e^{-\int_{t}^{T}r_s\,ds} X| \mathcal{F}_t\right]$

Imagine a model with stock prices and dividends of these stocks, as well as a market bond with associated short rate process. It is known that this model is arbitrage-free if there exists an ...
2
votes
3answers
176 views

Option greeks vs Position greeks

I know that when it comes to delta, you would calculate your position delta (of a stock position) as follows: option delta * position size * 100 For example if I ...
2
votes
1answer
217 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 ...
2
votes
2answers
172 views

Exercise on American call option and dividends

Consider an americal Call option on an underlying paying dividends. Then it is often argued that it is only optimal to exercise right before the dividend is paid out, otherwise one will not exercise. ...
2
votes
3answers
781 views

Daily option data

I am wondering where I can pull daily (hourly, by-the-minute, etc. even better) option data for a particular underlying. I would prefer a database I could scrape through and API, but would not mind ...
2
votes
2answers
562 views

SVCJ (SVJJ) Duffie et. al Model implementation in Matlab

I'm attempting to implement aforementioned SVCJ model by Duffie et al in MATLAB. so far without success. It's supposed to price vanilla (european) calls . parameters provided, the expected price is: ~...
2
votes
1answer
96 views

How do I prove that $\lim_{K\searrow0}\frac{P(K,T)}{K} = \mathbb P(S_T=0)$?

I am trying to prove that $$\lim_{K\searrow0}\frac{P(K,T)}{K} = \mathbb P(S_T=0)$$ where $P(K,T)$ denotes the put option price with maturity $T$ and strike $K$ for some stock $S$. Assuming interest ...
2
votes
2answers
141 views

When can a derivative be considered to be path dependant?

The typical example of path dependant derivatives are knock-ins and knock-outs. At the same time vanilla American options can also be considered to be highly path dependant. Does a more or less ...
2
votes
2answers
238 views

Options with a stochastic strike

Do options where the strike itself is a stochastic process exist? If they do - what are the motivations for such a product and where is it used ? Example: Call-Option with stochastic strike: $$(S_T(...
2
votes
2answers
3k views

Delta Neutral / Gamma Neutral Positions

I've been trying to find out more about options positions which are both delta neutral and gamma neutral--created with some kind of calendar spread. Supposedly, such a trade will be perfectly hedged ...
2
votes
2answers
168 views

Time-zero price of two specific contingent claims

I am unsure how to start with the following problem. I have two contingent claims where contingent claim (1) pays $\int_0^T S_u du$ and contingent claim (2) pays $(\log S_T)^2$ at time $T$ Now I ...
2
votes
2answers
1k views

Finding Probabilities Using The Binomial Model

I was not able to find a similar question when searching, but if I've missed one please feel free to point me to it. Unfortunately the closest example in the textbook was not terribly helpful either. ...
2
votes
2answers
399 views

Calculating Greeks in Covered Calls?

Just want to confirm whether Delta, Gamma, Theta, Vega will be calculated in the following way? Since we own 100 shares of stock while selling a call we need to subtract greek value from one? right? ...
2
votes
2answers
783 views

Index arbitrage with Options when not all underlyings have options listed?

One arbitrage strategy involves looking at the price of the Index Futures price compared with the prices of the options contracts for the underlyings. My question is, can this arbitrage strategy ...