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Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

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9 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?
201 views

Where can I find a clear explanation (brief derivation) of N(d1) and N(d2)?

Where can I find a good explanation (perhaps with a brief derivation) of N(d1) and N(d2) from Black-Scholes? Just trying to understand the general idea about these 2 probability functions and how they ...
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=...
1k views

Software for decomposing payoff diagrams into plain vanilla products

Nowadays structured products (or packages) with complex payoff diagrams are omnipresent. Do you know of any software, add-ons, apps, code whatever, that enables you to enter a payoff diagram or a ...
64 views

S. Bossu's Correlation Swaps Model

I am reading Sebastien Bossu's "A new Approach For Modelling and Pricing Correlation Swaps" (link). I am recalling some of the definitions from the paper and would like to understand how to prove one ...
254 views

Mixing Black Scholes with SABR

I am new to the whole concept of stochastic volatility so I am experimenting with option pricing. I think the concept is really difficult to understand / grasp. I was wondering if the following ...
44 views

Quesion about the VBA function of continuous cap look up [closed]

Here is the VBA function to calculate the cap price Can anyone tell me what is N and t0? From the textbook, N = the number of reset (or payment) dates and t0 = time until the first reset date. But ...
36 views

Pricing Equity Swaptions

Consider a swaption to enter into a standard equity swap as a fixed-rate payer, equity receiver, in which the notional principal is fixed. If the strike is K. the underlying swap starts at time 0=n ...
198 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 &...
95 views

A relatively useless but fun question for quants and physicists

Suppose I am a trader travelling in a very fast spaceship. What kind of SDE and corresponding PDE should I jot down and work with in order to ensure that there is no arbitrage (or if there is ...
41 views

European Call option replication

An asset $S_t$ is evolving according to the Black-Scholes model. We want to replicate a call option on this asset by holding Delta units of the asset at every time. I use a Monte Carlo algorithm to ...
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 ...
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 ...
48 views

155 views

Black-Scholes-Merton formula and option pricing

If the distribution is skewed to the right,Black-Scholes overprices out-of-the-money puts and in-the-money calls. It underprices in-the-money puts and out-of-the-money calls. How? Stock price log-...
44 views

Caplet price under stochastic volatility is the black price integrated over volatility distribution

Hull&White 1987 state that when the brownian motion driving the volatility and the brownian motion driving the forward rate are uncorrelated, the caplet price under stochastic volatility is the ...
66 views

Why and how is Implied volatility directly related to stock price but inversely related to strike price?

I know that in equity markets there is a volatility smirk which results in higher IV for lower strike price options because of crashophobia and leverage related factors but I can't wrap my head around ...
412 views

Why risk neutral probabilities should be strictly greater than zero for no arbitrage condition?

I was recently told by a colleague that the risk neutral probabilities should ALWAYS be greater than zero to have a no arbitrage condition. Intuitively, we know probabilities cannot be < 0, but how ...
1k views

Arbirtage free price process question in Bjork's Arbitrage Theory in Continuous Time

I am currently working through questions in Bjork's Arbitrage Theory in Continuous Time. However, I am unable to solve the following question, 7.2 in the book. A solution would be greatly appreciated. ...
58 views

Can someone provide a good definitive explanation for rho in relation to option risks?

I have a pretty good understanding of option risks except for one thing, rho. Unfortunately, interest rates tend to have a small effect on option prices, and thus most literature tend to just gloss ...
130 views

theoretical reason for which we can use monte carlo simulation for option pricing

The classic way to price an option is solving either analitically or numerically the associated PDE subject to the terminal and boundary conditions. An alternative approach is to use monte carlo ...
831 views

Monte Carlo method vs PDE in option pricing

Good evening everyone, I would like to ask a question about Monte Carlo and PDE Pricing. For an American option, which one should we use, Monte Carlo method or PDE method? The same question for an ...
283 views

How to calculate return on investment for an adjustment to a complex options position?

Say I currently hold a set of options positions with the same symbol/expiry that collectively have a net present value based on the estimated value at expiration of +10. I could also liquidate the ...