Questions about models for the valuation of option contracts.

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7
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2answers
191 views

How to price an option allowing to change a call into a put?

A recruiter asked me this question: Suppose you have the following contract: a call option with maturity T = 2 years the possibility to change this call into a put at t = 1 year What is the price ...
0
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0answers
22 views

Price of call (calibration)

I need to understand how we got this : $\forall i \in I $ $C^{*}_{0}(T_i,K_i)=e^{-rT_i}E[(S_{T_{i}}-K_i)^+|S_0]=e^{-rT_i+X_{T_{i}}}E[(S_{T_{i}}-K_i)^+]$ at How we pass from conditional expecation to ...
1
vote
2answers
111 views

Pricing Forward Start Option with PDE

I am looking for references (books and papers) or suggestions on how to price forward starting calls using a PDE approach typically in the Heston model (In the BS world, the computation is trivial), ...
2
votes
0answers
73 views

Example of optimal delta hedging in G. Barles, H.M. Soner option pricing paper

There is a paper Option pricing with transaction costs and a nonlinear black-scholes equation by Guy Barles and Halil Mete Soner. And there is a section about optimal (delta) hedging, which I do not ...
2
votes
1answer
539 views

Black Scholes - how to calculate delta with a vol skew

I am trying to calculate the delta of an option at different strike prices where the underlying has a pronounced implied volatility skew in order to correctly hedge an options strategy. Researching ...
3
votes
3answers
138 views

How to price a path dependent exchange option using?

Assume you have two stocks $S$ and $P$ so that at initial time $t = 0$: $S_0 > P_0$. You bought an option which pays off $S_T - P_T$ as long as $S_t > P_t$ through the time $0 < t < T$. ...
1
vote
2answers
89 views

Fourier Transform

In a notes on "Option Pricing using Fourier Transform": Price of plain vanila call is given by $$ C(t, S_t) = e^{-rT}\mathbb{E}^{\mathbb{Q}}[(S_T -K)^+|\mathcal{F}_0] = e^{-rT} \int_K^{\infty} (S_T ...
0
votes
1answer
38 views

Swaption on a swap with 0 year tenor

Any ideas on valuation of IRS swaption on a swap with 0 year tenor? As an example, we have a 5 year swaption, on expiration it is cash settled; the underlying swap tenor is 0 years with excercise and ...
1
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1answer
44 views

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 ...
0
votes
0answers
28 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 ...
0
votes
1answer
77 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 ...
0
votes
1answer
106 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 ...
1
vote
1answer
54 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 ...
0
votes
0answers
25 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 ...
1
vote
1answer
64 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 ...
0
votes
1answer
95 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 ...
1
vote
1answer
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 ...
8
votes
3answers
630 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 ...
0
votes
1answer
63 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} = ...
1
vote
1answer
97 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 ...
0
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0answers
40 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 ...
2
votes
0answers
45 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 $0 < d < 1 + r < u$. ...
1
vote
2answers
278 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 ...
0
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0answers
42 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 ...
1
vote
1answer
53 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 ...
4
votes
3answers
192 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 ...
2
votes
2answers
261 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 ...
1
vote
1answer
49 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 ...
7
votes
0answers
197 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: ...
3
votes
1answer
85 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: ...
1
vote
1answer
79 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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0answers
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 ...
2
votes
3answers
186 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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0answers
83 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? ...
8
votes
1answer
210 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 ...
2
votes
2answers
233 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 ...
16
votes
9answers
6k 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 ...
2
votes
0answers
61 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 ...
1
vote
1answer
95 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 ...
2
votes
2answers
76 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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0answers
31 views

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 ...
0
votes
1answer
67 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 ? ...
0
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2answers
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 $t=0$?
4
votes
5answers
5k views

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 ...
2
votes
1answer
84 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 ...
1
vote
1answer
198 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 ...
0
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0answers
73 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 ...
3
votes
1answer
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 ...
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1answer
60 views
0
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1answer
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 ...