Questions about models for the valuation of option contracts.

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How to Calculate Return Option with Forward Measure

I am trying to computing the price of an option at time $t$, with payoff $X = \frac{S_{T_2}}{S_{T_1}}$, at time $T_2$, where $t < T_1 < T_2$. Here how I compute it: Using the forward measure $...
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33 views

Solving Black Scholes PDE using Laplace transform with barrier up and in, up and out call option

I tried to finish the option pricing in european barrier up and in, up and out call option using Laplace transform. The barrier option there is a boundary condition. Can you explain step by step ...
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79 views

Calculating the volatility for Black Scholes

The following problem is from the book by Hull. I did it but I am not sure it is right. I am hoping that somebody here can tell me if I did it right and if not where I went wrong. Thanks Bob Problem:...
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118 views

Can someone explain to me what's snell envelope?

What is snell intuitively? And what is its use in quantitative finance? Please explain to me as intuitive as possible! As I explained in the comments, I am new to this field and I was hoping someone ...
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55 views

When to include dividends in option valuation

When using the Black-Scholes-Merton method for option valuation which takes into account dividends, does the dividend only get included into the calculation of options whose lifetime straddles the ...
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29 views

Two-period pricing of a European put via riskless portfolio

The current price of a stock is $40. It is known that it either increases or decreases by 12.5% every 3-months over the next 6-month period. The risk-free rate of interest is 8% per annum (continuous ...
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80 views

Call and Put Prices Equal at Forward Price - Why?

Consider a European call and put with values $C_t$ and $P_t$, respectively, under the Black-Scholes model. By put-call parity, $$ C_t - P_t = S_t - Ke^{-r(T-t)} $$ for expiration time $T$. Note if $...
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101 views

Does the fact that volatility is not constant imply existence of skew?

I had a question regarding the existence of the volatility skew. I've tried researching it a fair bit and I come across a few different explanations: 1. Market participants like buying downside puts ...
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110 views

Use of Black-Scholes Model on Guaranteed Fund Investment

I am stuck with a revision question at home on Black-Scholes pricing model. The question is on a fund manager selling one unit of the fund to a customer for $S(0)$ at time $0$ and then guaranteeing ...
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638 views

Is the price of European put option monotone in volatility if we replace BM in Black-Scholes with a general Levy process?

Under the Black-Scholes model, we have the European put option is $\mathbb{E} [e^{-rt}(K-S_t)]$, where we take $\log(S_t)=X_t$ and $dX_t= \sigma dW_t - \dfrac{1}{2}\sigma^2 dt + rdt$. Here the option ...
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64 views

Finding circumstances for price of call = price of put

Here is a problem in Hull's book and the given solution: My approach was to compute the profit $\pi = \pi_{SP} + \pi_{LC}$ (short put, long call). One can show that $\pi = \pi_{SP} + \pi_{LC} = ...
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106 views

How to price touch options using quantlib?

I am new to quantlib and I want use it to to price a touch option (single/double). I searched on google for example code but I could not find anything. Hence, I am ...
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44 views

Price a Fixed Strike Lookback Call Option

I'm having an issue working out the following: Consider a three-period asset price model with interest rate 1+r =6/5 in each period. The initial price of the asset is 4 dollars, while in each period ...
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48 views

Does the Binomial Pricing Model require a no-arbitrage assumption?

In a binomial option model, if we take the uptick as 6%, downtick as 5% (assume equally probable), and RFR of 6% (continuous compounding), then we have a violation of $0 < d < 1 + r < u$. ...
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321 views

Vega hedging with implied volatility smile

I have a problem with vega hedging. Consider the management of an exotic derivative, such as Barrier option. Typically we do the following tasks: selecting a pricing model, say, a local volatility ...
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47 views

How to find the fx lookback floating/fixed strike options prices?

Currently, I'm working on my thesis in which I'm trying to describe how are the FX lookback options priced. I need to find the real ...
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1answer
56 views

Applying interest rate models for volaility rate

To what extent may the interest rate models be applied for modeling implied volatity? The story: I was checking different stochastic option pricing models for being able to replicate implied ...
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210 views

Can I get Black-Scholes option price from greeks?

I am unpleased with current Interactive Brokers risk graph for option strategies, so I'm planning on writing an application myself to plot it. My initial idea is to get the option greek values from ...
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2answers
277 views

Why do we need $dS_t=r S_tdt+\sigma S_tdW_t^Q$?

Suppose $S_t$ is the stock price and follows the dynamics $$dS_t=\mu S_tdt+\sigma S_tdW_t$$. According to Girsanov, we can apply change of measure and obtain $dS_t=r S_tdt+\sigma S_tdW_t^Q$, this ...
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50 views

How do I incorporate dividends into options pricing

-Hey all, recently I encountered the necessity to incorporate dividends into options pricing. Lets say I have the following american put option: Initial price - 100, T-0.25, Volatility is 30%, Number ...
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205 views

Max option leverage strike

Since options represent leveraged stock investments, at which strike $K$ does a European option provide maximum leverage? Hereby define leverage $L$ as ratio of Delta/Optionprice: $$L(K)=\frac{\...
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92 views

Derivation of Magrabe formula

I'm going through the following note by Davis, link. In chapter 3 he derives the Magrabe formula. I got stuck at equation $(3.16)$. We have two assets: $$dS_i(t)...
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80 views

What is more likely effect to call and put prices, respectively, if the stock price decreases by$1?

The current stock price is \$80.Call ,and ,put, options, with ,exercise ,prices, of $50 and 3 days to maturity are currently trading. What is more likely effect to call and put prices, respectively, ...
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18 views

Pricing claims of parties in a fund

I'm working on the following problem and would appreciate some input because I'm stuck. Consider a fund that works as follows. The fund starts with $S_0$ worth of assets following a geometric ...
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188 views

Analytical soluton to the Black-Scholes equation with a modified European Call Option

Please consider the following modified European Call Option where $ 0 < a \leq 1$. When $a = 1$ the modified European call option is reduced to the standard European call option. ...
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85 views

Which option pricing models agree best with the market, given the asset price is known?

Assuming you can somewhat forecast the underling asset price movement, and you want to translate this value into the corresponding option price. In practice, which are the better models for this task? ...
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216 views

Time value of option not always leading to an increased option value

My understanding was that as you increase the time to expiry of an option, the value of the option increases. However, I have run a bunch of scenarios and have realized that if you assume a dividend ...
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237 views

Exercise 2.2 from the book “The concept and practice of Mathematical Finance”

I am a newbie. Please help me understand how to resolve the exercise 2.2 from the book "The concept and practice of Mathematical Finance". The solution from the book says that our super-replicating ...
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9answers
7k views

Why Drifts are not in the Black Scholes Formula

This question has puzzled me for a while. We all know geometric brownian motions have drifts $\mu$: $dS / S = \mu dt + \sigma dW$ and different stocks have different drifts of $\mu$. Why would ...
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62 views

How can the time value portion of an option be higher than 100%?

Here's a screenshot from InteractiveBrokers TWS for the near-the-money put and call on the ES Dec '15 Future: The absolute value of the time value, 9.50, makes sense. But why is the percentage ...
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107 views

Delta hedging cost of exotic options?

I'm simulating dynamic delta hedging for up-and-out call option. For plain vanilla call options, I heard that the option price is the expected value of the accumulated delta hedging cost. Does it also ...
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77 views

Volatility of Multiple Stocks

According to BSM, Stock Price follows log-normal distribution s.t. $$S(t)=S(0)*\exp(\sigma\sqrt t Z-(\sigma^2t)/2)$$ where Z is standard normal variable Then volatility of this stock is $\sigma \sqrt ...
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Jacobian for Newton method for American options by front fixing

In this paper Penalty and front-fixing methods for the numerical solution of American option problems a front fixing method based on Newton is described for an American put option is described. I am ...
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72 views

Binary Option valuation problem in R using RQuantLib; also result validation aspect

When I am trying to value Binary Option using RQuantLib I am not getting all the greeks for exctype "american" wheras "european" exctype is fine. What is the problem here ? ...
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104 views

Why the value of this portfolio is negative? [closed]

Let's assume I buy 1 call with strike 100 and 1 call with strike 120 I sell 2 calls with strike 110 (with same expiration) I wonder why value of this portfolio is negative at $t=0$?
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Risk Neutral Probability

I read that an option prices is the expected value of the payout under the risk neutral probability. Intuitively why is the expectation taken with respect to risk neutral as opposed to the actual ...
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90 views

CallableFloatingRateBond in QuantLib: just a matter of multiple inheritance?

I would like to know what are the issues related to a possible CallableFloatingRateBond class in QuantLib and to have some hints on implementation. My (very ...
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205 views

Local volatility pricer

I am testing a local volatility pricer by comparing its results under two settings: Pricing a 5yr ATM call option with a flat volatility of $0.194$ Pricing the call option with the typically shaped ...
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74 views

Discrete Hedging of Options

Assume that a stock $S_t$ follows simple geometric Brownian motion. Let's say we sold option whose payoff is $f(S_T)$. Now, we are only allowed to trade 2 times in the interval [0,T]. What kind of ...
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114 views

How to calculate $E^{T_N}(L(T_i, T_{i+1}))$?

suppose $L(T_i, T_{i+1})$ is the LIBOR rate between $T_i$ and $T_{i+1}$, and $T_N$ is some time later than $T_{i+1}$. $E^{T_N}$ is the $T_N$-forward measure. I tried to work this out using John Hull'...
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100 views

Do I need simulink to model the risks of an option portfolio

I wish to buy Matlab Home and learn to model the risks of a derivatives portfolio and then stress test it. So I am guessing I will need : Stochastic calculus Linear algebra Stats/Probability Some ML ...
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82 views

Numerical computation of Heston model Integral: Simpsone Rule or Gauss-Legendre Method

I want to price a call option using the Heston model for a given set of parameters. theory from URL: http://elis.sigmath.es.osaka-u.ac.jp/research/Heston-original.pdf The integral equation (18) ...
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2answers
531 views

Why does changing the time step size in my Monte Carlo simulation change my result a lot?

I have written some software to price a call option using Monte Carlo simulation. It produces a price which is consistent with the model when I set the time step as recommended in a tutorial that I ...
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77 views

Approximate asian geometric option with Heston

I am trying to implement Theorem 1 from this Journal in RStudio. The journal says the it is possible to find a approximate price of a geometric asian option in a Heston setup this way: $$X_{1cGAO}=e^{...
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201 views

Feynman Kac Formula for path-dependent options

Consier geometric Brownian motion: $dS_t/S_t=\mu dt+\sigma dW_t$ Feynman Kac theorem tells us that the conditional expectation $v(t,x)=E[ e^{-rT}\Psi(S_T) | S_t=x]$ can be computed by solving the ...
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159 views

Option with payoff $K^2/S^2$

Given the dynamics of the risky asset ( with dividend $q$ ), $$ \frac{dS_t}{S_t}=(\mu-q)dt + \sigma dW_t^P $$ Consider a european option with payoff, $$ P_0(S) = \begin{cases} 1, & \text{...
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116 views

When valuing a vanilla option on an index, should we take dividend into account?

When valuing a vanilla option on an index (eg FTSE 100), should we take index dividend yield into account? $$ c=Se^{-q\tau}N\left(d_1\right)-Ke^{-r\tau}N\left(d_2\right) $$ $$ d_1=\frac{\ln\left(\...
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82 views

Pricing employee stock options

ESOs are typically priced using the black-scholes model, but with an additional parameter for for the employee turnover rates . An example http://www.investopedia.com/university/employee-stock-...
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119 views

How to value a Binary Option using market data?

Is there a way to calculate the price of a binary option (i.e., an option that pays out 1 dollar when the stock price hits $x$ amount) using market call/put option prices, forward prices, etc. for a ...