European call option with ination-linked strike

2004

In spite of the power of the Black & Scholes option pricing method, there are situations in which the hypothesis of a lognormal model is too restrictive. One possibility to deal with this problem, consists of a weaker hypothesis, fixing only successive moments and eventually the mode of the price process of a risky asset, and not the complete distribution. The consequence of this generalization is the fact that the option price is no longer a unique value, but a range of several possible values. We show how to find upper and lower bounds, resulting in a rather narrow range. We give results in case two moments, three moments, or two moments and the mode of the underlying price process are fixed.

SSRN Electronic Journal, 2015

Background We define a family of models where the evolution of the price process S(t) is given by the system of stochastic differential equations where σ is a twice continuously differentiable function, and δ, r and θ are constants for the dividend rate, the short interest rate and the market price of risk. We prove that as long as σ (•) satisfies a behavior defined by Eq. (11) below, the given system of differential equations describes a global solution (with non-explosion). The existence of a suitable solution is discussed since in the presented setup is not restricted to Lipschitz coefficients. We also prove that the market with stock whose price evolution is given by S(t) and short interest rate r is free of (state) arbitrage opportunities; in addition as long as dσ (•)/dx satisfies the non-singularity condition given by Eq. (12) the market defined above is (state) complete. The definitions of (state) completeness and (state) arbitrage opportunities are new and developed by the author (Londoño 2004). We also analyze the empirical behavior whenever σ (x) = n 2 (P − x), and θ = n 1 /n 2 where n 1 , n 2 , P are constants; this family has a simple economic interpretation [see remarks make after dS t = (σ (Ŝ t)θ − δ + r)S t dt + σ (Ŝ t)S t dW t S 0 = s 0 dŜ t = −δŜ t dt + (σ (Ŝ t) − θ)Ŝ t d W tŜ0 = s 0 .

Insurance: Mathematics and Economics, 2007

Nobody doubts the power of the Black and Scholes option pricing method, yet there are situations in which the hypothesis of a lognormal model is too restrictive. A natural way to deal with this problem consists of weakening the hypothesis, by fixing only successive moments and possibly the mode of the price process of a risky asset, and not the complete distribution. As a consequence of this generalization, the option price is no longer a unique value, but rather a range of possible values. In the present paper, we show how to find upper and lower bounds for this range, a range which turns out to be quite narrow in a lot of cases.

2004

We present a European call option that is defined on a pension annuity insurance contract. This option gives the holder of the contract the opportunity to buy a pension annuity benefit for a given (strike) price at the age of retirement or any other age. Thus instead of contributed monthly payments to the pension fund, the holder of the option

Applied Mathematics and Computation, 1999

In this paper, we propose a new model for the (B,S)-market in which the stock price and the asset in the riskless bank account have hereditary price structures. Speci®cally, the dynamics of the stock price and the bank account are described by linear stochastic functional dierential equations. The pricing of the European contingent claims is studied and the corresponding trading strategy is derived.

Journal of Financial Economics, 1976

pricing of simple put and call options lay !he foundation for the development of a general theory of the valuation of contingent claims assets. This paper provides a review of: (1) the development of the general equilibrium option pricing model by Black and Scholes. and the subsequent modifications of this model by Merton and others; (2) the empirical verification of these models; and (3) applications of these models to value other contingent claim assets such as the debt and equity of a levered firm and dual purpose mutual funds.

SSRN Electronic Journal, 2000

A derivative security is a contract whose payoff depends on the stochastic price of another security, called an underlying asset. For example, consider a contract which gives you the right to sell a share of IBM stock in three months for $100. This contract, called European put option, provides you with an insurance against IBM stock price dropping below $100. In three months, if IBM stock price, S IBM < $100, you can buy IBM stock for S IBM and exercise the option, selling the stock for $100, and pocketing the difference $100 − S IBM . If IBM stock price is S IBM ≥ $100, you allow the option to expire unexercised. What is the "fair" price for this put option today? In this article we will describe models, theory, and numerical methods for pricing derivative securities.

With reference to a European call option, under normal conditions, the behaviour of a writer is like that of an insurer making probabilistic estimates of the value of a share at expiration and deducing the price at which the option should be offered. This paper presents a method of constructing the random share value variable based on a three-state Markov process and numerical aspects of the option price from the point of view both of “equity” and “expected utility”.

2016

In this paper we consider the European continuous installment call option. Then its linear complementarity formulation is given. Writing the resulted problem in variational form, we prove the existence and uniqueness of its weak solution. Finally finite element method is applied to price the European continuous installment call option.

AnandaPutriSyaviri 130533608243 S1 PTI'13 OFF B UNIVERSITAS NEGERI MALANG FAKULTAS TEKNIK JURUSAN TEKNIK ELEKTRO PRODI PENDIDIKAN TEKNIK INFORMATIKA Oktober 2013 ARRAY A. Tujuan Setelah mempelajari bab ini diharapkan mahasiswa akan mampu : 1. Mengenal dan memahami penggunaan array dalam listing program. 2. Membuat program sederhana dengan menerapkan konsep array. B. ARRAY Array adalah kumpulan dari nilai-nilai data bertipe sama dalam urutan tertentu yang menggunakan sebuah nama yang sama. Nilai-nilai data di suatu array disebut dengan elemenelemen array. Letak urutan dari elemen-elemen array ditunjukkan oleh suatu subscript atau indeks. 1. ARRAY DIMENSI SATU a. Setiap elemen array dapat diakses melalui indeks b. Indeks array secara default dimulai dari 0. c. Deklarasi array dalam bentuk umum: Tipe_array nama_array[ukuran]; Contoh : int Nilai [4] Nilai [0] Nilai [1] Nilai [2] Nilai [3] 70 80 82 60 2. ARRAY DIMENSI DUA Array dua dimensi merupakan array yang terdiri dari m buah baris dan n buah kolom. Bentuknya dapat berupa matriks atau tabel. Bentuk Umum: Tipenama_array[baris][kolom]; Contoh: