Introduction to stochastic programming and its applications to finance

Mathematical programming is one of a number of operations research techniques that employs mathematical optimization models to assist in decision making. Mathematical programming includes linear programming, integer programming, mixed-integer programming, nonlinear programming, stochastic programming, and goal programming. Mathematical programming models allow the decision maker to identify the “best” solution. This is in contrast to other mathematical tools that are in the arsenal of decision makers such as statistical models (which tell the decision maker what occurred in the past), forecasting models (which tell the decision maker what might happen in the future), and simulation models (which tell the decision maker what will happens under different conditions). The mean-variance model for portfolio selection as formulated by Markowitz is an example of an application of one type of mathematical programming (quadratic programming). However, in formulating optimization models in many applications in finance, the mathematical programming model employed needs to take into consideration the uncertainty about the model’s parameters and the multi-period nature of the problem faced. To deal with these situations, the technique of stochastic programming is employed

"Türk usulü" portföy sigortası: anapara koruma amaçlı yatırım fonları (Portfolio insurance "alla Turca": capital-protected mutual funds)

Portföy sigortası stratejileri, gelişmiş finansal piyasalardaki yatırımcılar tarafından 1980’lerin başlarından beri uygulanmaktadır. Bu çalışmada, bu stratejilerin Türk yatırımcısı tarafından kullanılabilmesi için 2007 yılında yeni bir yatırım aracı türü olarak ortaya çıkan anapara koruma amaçlı/garantili yatırım fonları incelenmektedir. Bu amaçla, Ekim 2007-Mayıs 2010 arasında halka arz edilmiş ve bu kategoriye ait 99 yatırım fonu ile ilgili veriler derlenmiş, ürünlerin zaman içerisinde değişkenlik gösteren özellikleri belirlenmiş ve getiri performansları hesaplanmıştır. Her bir yatırım fonunun getirisi aynı dönemlerde klasik yatırım araçlarıyla elde edilebilecek getirilerle karşılaştırılmış ve bu ürünleri bireysel yatırımcıların ve reel sektör önderliğindeki kurumsal/ticari yatırımcıların kullanımına sunan finans sektörünün optimal ürün tasarımı konusundaki başarısı incelenmiştir

Pricing bundled options in supply chain contracts

In this paper, for a supply chain contract, we design and value a bundled option that is composed of contract abandonment and price renegotiation. We numerically show that the bundled option is more valuable for the contract than either of the options, i.e., contract abandonment and price renegotiation, in isolation. This value increases monotonically as the spot price becomes more volatile. The value of the bundled option is less than the sum of the individual option values, hence showing the sub-additive property. We demonstrate that in the presence of high spot price volatility, the bundled option is more valuable when renegotiation date is selected to be closer to the half-life of the contract. We also show that early contract abandonment probability goes down in the presence of renegotiation option. We conclude that the commodity supplier should negotiate a supply chain contract with flexible options at the design stage with the buyer, obtaining contract abandonment and price renegotiation options –as a bundled option—in order to enhance the supply contract value and reduce the contract breach risk