Questions tagged [put-call-parity]

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Prove the following Call and Put relationship: [duplicate]

I need to prove that $$c(S,X,T)=\frac{X}{F}p(S,\frac{F^2}{X},T)$$ where $$F=Se^{(r-q)(T-t)}$$ I am having trouble proving this relationship. Is this relationship even possible? If so, can someone ...
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38 views

Put-call parity for equity share and debt share

Considering Merton's structural approach" for credit risk modeling, we arrive to prove that the pricing formules are $S_t=V_t\phi(d_{T,1})-Fe^{-r(T-t)}\phi(d_{T,2})$ for equity share and $F_t=FP_0(t,T)...
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1answer
59 views

Why do we need to borrow money in the call-put parity? [closed]

As I understand it, the call put parity is given by $$c = p + S - \frac{X}{(1 + r)^T}$$ I understand the rationale behind simultaneously buying the call, put and underlying asset for $S$, but why ...
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0answers
71 views

What are the main problems for calculating the implied volatility of in the money American put options?

As stated in the question I have a problem with calculating the implied volatility for in the money put options I have a data set of 2.6 million American style plain-vanilla call and put options. For ...
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2answers
177 views

Why do I get a curved line when I plot “implied interest rate” on the strike price?

Currently, I am working on my thesis (MSc. Finance) and I run into an interesting “phenomenon”. I have option data for a non-dividend paying stock. In class I have learned, how to calculate the ...
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0answers
52 views

Is it necessary for $P(K, t) - P(K + s, t) \geq se^{-rt}$ to hold?

Let $P(K, t)$ be a put option with strike price $K$ and expiration time $t$. Let $s > 0$. Is it necessarily true that the inequality $$P(K, t) - P(K + s, t) \geq se^{-rt}$$ holds? I know that ...
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1answer
56 views

How to get Forward price based on Put-Call parity?

Could you advise how to find a forward price using Call/Put (+Spot and Strike) ? Investodepia says that forward is equal to option's strike based on Put-Call Parity but it seems to me there is a ...
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1answer
102 views

Bermudan Swaption

Is there an equation of the kind of call-put parity for Bermudean swaptions ? (maybe an inequality ) Is there an intuitive description of what would be an optimal exercise moment ? Intuitively I ...
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2answers
51 views

Construct a portfolio of European call options with a certain payoff function

My question is similar to Replicate a Portfolio with Given Payoff but I am not quite sure how to apply this to my problem. A portfolio of European call options on an asset $S_T$ has a payoff ...
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1answer
44 views

Determine the maximum arbitrage profit from the given contracts

I really have tough time trying to figure this out. An investor observes the following prices in the market: Euro-Stoxx-Future DEC 148.02-148.03; Euro-Stoxx-Future Call-Option DEC 148.00 1.13-1.15; ...
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61 views

Implied Funding/Borrow Costs in Short-Dated ETF Option Prices

I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
2
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1answer
119 views

Should Put/Call Parity result in Zero Return or the Risk-Free Rate?

Sorry in advance if this is a basic question. I'm examining some potential at-the-money put/call arbitrage. What I found surprised me somewhat: ...
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1answer
64 views

Call Option Overvalued and put-call parity [closed]

I have a question regarding if a Call option is overvalued compared to the call price and how you can benefit from the Arbitrage opportunity. My thoughts are as follows: Step 1: Short the call ...
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1answer
108 views

Is there an advantage trading options based on deep in the money Open Interest Volume ratio

Problem: Deep in the money options contracts will be assigned at expiration date. Higher Volume ratio of deep in the money contracts at expiration calls or puts leads to day after expiration date we ...
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1answer
84 views

Decreasing value of the Put option with increasing Time to maturity [closed]

Can you think of a situation when increasing the time to maturity lowers the value of a put option? If yes, show the example pls.
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1answer
128 views

Risk of Put-Call-Parity in practice

When $C+PV(K) \ne P + S_0$, it's an opportunity for risk-free arbitrage (excluding cost). In practice, what potential risk could make the arbitrage fail? I know that failure to build complete ...
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1answer
100 views

Equity repo close to money market rates?

I've noticed that the repo rate (here I mean the effective financing rate of the forward position in stock) implied from synthetic forwards is almost the same as money market benchmark (XXXibor 3M) ...
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2answers
1k views

Put-call parity for cash settled swaptions

The Euro swaption market is changing from cash to physical settlement quotation in July 2018 $-$ see e.g. "Euro swaptions market prepares for pricign revamp (Risk, 2018)". When describing the issues ...
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3answers
516 views

Put Call Symmetry

I want to show the Put Call Symmetry without using the explicite Black Scholes formula. In other words I want to show Call(t, x, K, T) = Pull(t, K, x, T) where $S_t = x $ for $t \in [0, T]$. I ...
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55 views

Different versions of Put-Call Parity

Why is it stated sometimes that $C - P = F$ and in wikipedia it statest that $C - P = D(F-K)$, where D is the discount factor and K is the strike (of both the call and put?). Is this just affected ...
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223 views

Understanding put-call parity

I'm a person with math background trying to break into quantitative finance, and there's something about put-call parity that is not making sense to me. Below I'll detail my understanding of the ...
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1answer
281 views

Interpretation and intuition behind the Put-Call symmetry under the Heston Model

I am currently working on a report regarding the put-call symmetry relations under the Heston model. I did all the math and managed to prove the relations using PDE approach. However, I wish to have a ...
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1answer
237 views

Question about the vega of a stock

In Black-Scholes model with constant parameters, a call and a put with the same characteristics have the same vega: https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model#The_Greeks Using call-put ...
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241 views

Convexity of Call option prices using Put-Call parity relationship

I am trying to price vanilla options using a particular Bayesian approach that I have found in a paper. To do that I need to construct a likelihood function, approximating the tail of the distribution ...
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1answer
310 views

Violation of the call-put parity

The last price of Wells Fargo (Ticker: WFC) on Thursday, 10/26/17, was $55.62. Options with expiration 11/17/17 had following last prices: Options with expiration 11/17/17 had following last prices: ...
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2answers
192 views

Is an options implied dividends DCF model consistent with risk neutral/arbitrage-free valuation?

We're talking about how we price every financial instrument: by discounting the payoff, that is, we take future cash flows and we discount them by a proper rate which takes into account the risk of ...
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2answers
635 views

Implying risk-free rates using Put/Call parity

I recently purchased SPX options data from the CBOE. Normally, if the data is OK and the Put-Call parity holds, one should expect to correctly imply ZC (Zero Coupon bond) prices and forwards by ...
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1answer
213 views

Put-Call Parity on Currency and Binomial Trees

I tried solving the below problem without knowing the shortcut of thinking about this in terms of a put versus a call. I can't seem to arrive at the correct answer using my method and I'm wondering ...
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3answers
3k views

Relationship between forward and option prices

Do forward prices factor into option prices at all? It seems to me from Black-Scholes that you just need a spot price and interest rate r. I understand that $F_t = S_0 e^{r t}$, but I don't know if ...
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1answer
412 views

Build a Synthetic Loan for Personal Finance

Suppose I am short of cash and want a loan for some mundane objective like travelling or buying a car. The interest rate for personal loan with my bank is too high. Is there any way in finance that ...
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3answers
671 views

At the money put and call having the same price

This is a commonly asked question and I have not been able to find a satisfactory answer to it. Let me first phrase it here. Suppose that interest rates are $0$ and consider an at the money put and an ...
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1answer
143 views

How far the spot price is likely to go from the current level in three months if its volatility is 15.7%

On Page 24 of N. Taleb's "Dynamic Hedging" the author gives the following example Example: Assume that an asset trades at \$100, with interest rates at 6% (annualized) and volatility at 15.7%. ...
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2answers
502 views

Prove that the vertical spread condition is bounded

I need to prove that vertical spread is bounded, by using no arbitrage condition. 0 > (C(T,K1 )- C(T,K2))/(K1- K2 ) >-e^(-r*T ) I have documented my ...
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28 views

Best strategy for generating floats with minimum amount of risk

I'm looking for a way to get cash-in-hand in exchange for future obligation. For example, I can sell deep-in-the-money puts and buy out-of-the-money puts (for hedge) with expiration of 2 years, The ...
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1answer
75 views

Is it possible to calculate the call-put parity for an option's portfolio?

Let's say I have designed an option's portfolio. The portfolio includes long as well as short positions in European-style put and call contracts based on the same underlying asset with different ...
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1answer
139 views

Is this representation of the put-call parity correct? (Implied dividend estimation)

I am looking at implied dividend yields to be obtained from the put-call parity and have come across the following answer: Implied dividend estimation It states that $$ PV(div) = P - C + (S - K) + K(...
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1answer
99 views

Put call parity: when are the premiums the same?

Please explain why put call parity could be compared to the payoff of a long forward contract. ie. $C_E-P_E=V_X(0)$ where $C_E,P_E$ are the call/put premiums and $V_X(0)$ is the value of a long ...
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3answers
626 views

Construct option and stock portfolio

If a riskless security costs 100 today and will cost 120 at time T, a stock costs 50 today and will either be 70 or 30 at time T, and call options on the stock have strike price 50 expiring at time T, ...
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3answers
273 views

Put-Call Parity Application

In the binomial model, how that the Delta of a call option $\Delta^{call}$ and the Delta of a put option $\Delta^{put}$ with the same maturity and strike satisfy $$\Delta^{call}_t - \Delta^{put}_t = ...
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1answer
61 views

Understanding the necessary and sufficient conditions for rational early exercise of a call option

I am self-studying for an actuarial exam, and I encountered the following in my text: The author states that if $PV_{t, T}\text{(Divs)} < K(1 - e^{-r(T - t)})$, early exercise is not rational. ...
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4answers
2k views

Difficulty understanding put-call parity for currency options

I am self-studying for an actuarial exam on models for financial economics. I am having difficulty thinking about the put-call parity for currency options, specifically how use the notation. Here is ...
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1answer
94 views

Problem solving using the put-call parity

I am self-studying for an actuarial exam on financial economics. I encountered this problem, and I am having difficulty seeing why the statement underlined is true: How do we know that $P(60) - C(60) ...
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1answer
91 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
228 views

Logic between options and risk free rate [closed]

What is the relationship between put option price and risk free rate? And between call options price and risk free rate? Explain the logic? No calculation.
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0answers
30 views

Financial Derivative, European Option [closed]

Market Prices for European put and call options on ABC stock are as below: Call = $4.5 Put = $6.8 Exercise Price, X =$70 Risk Free Annual Compounded rate r = 5% Time to expiration T = 139 days ...
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2answers
839 views

put call parity for futures options derivation in Hull

In Hull, the following derivation of PCP for futures options: What confuses me is that it is stated that the payoff of the long futures is $F_t-F_0$. The footnote states: the analysis assumes that a ...
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1answer
875 views

Put-Call Parity Arbitrage Exploitation for Binary-Asset-or-Nothing Options

Is the Put-Call-Parity valid for binary (asset-or-nothing) options? If not, is there another formula for such exotic options? I know that for regular options, there are arbitrage opportunities when ...
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1answer
3k views

Why is IV different between put and call of same strike

In his book 'Dynamic Hedging' Nassim Taleb says that the volatility of an OTM put should be exactly equal to that of a corresponding in the money call of same strike. But in option chains, the ...
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1answer
260 views

PWIQF excercise solution

I am software developer with no previous experience or knowledge in finance and have recently been starting to build my knowledge in this area. I am working through the book: Paul Wilmott Introduces ...
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1answer
595 views

Risk-free investment strategy for european call and put option

I have some trouble solving the following question: We have an european call and put option (with the same maturity date $T$ en strike $E=10$). The stock price now is $S=11$ and we use a continuous ...