I denna uppsats skapar vi en modell för forwardkurvan på den nordiska elmarknaden. Vårt mål är attskapa en modell som är lättanvänd och inte kräver kunskaper om dynamiken hos elpriset. Vår modellär baserad på en modell av Benth, Koekebakker & Ollmar (2007) men justeras med avseende på vårakrav om en lättanvänd modell. Vi validerar vår modell och nner att den har möjlighet att föutspåpriset på ett kvartlaskontrakt med en felmarginal på 1.1 procent. Vi lyckas förutspå en säsongsvariationutan att specikt ange en funktion för säsongsvariationen.

This thesis consists of three essays on risk management in crude oil markets. In the first essay, the valuation of an oil sands project is studied using real options approach. Oil sands production consumes substantial amount of natural gas during extracting and upgrading. Natural gas prices are known to be stochastic and highly volatile which introduces a risk factor that needs to be taken into account. The essay studies the impact of this risk factor on the value of an oil sands project and its optimal operation. The essay takes into account the co-movement between crude oil and natural gas markets and, accordingly, proposes two models: one incorporates a long-run link between the two markets while the other has no such link. The valuation problem is solved using the Least Square Monte Carlo (LSMC) method proposed by Longsta ff and Schwartz (2001) for valuing American options. The valuation results show that incorporating a long-run relationship between the two markets is a very crucial decision in the value of the project and in its optimal operation. The essay shows that ignoring this long-run relationship makes the optimal policy sensitive to the dynamics of natural gas prices. On the other hand, incorporating this long-run relationship makes the dynamics of natural gas price process have a very low impact on valuation and the optimal operating policy. In the second essay, the relationship between the slope of the futures term structure, or the forward curve, and volatility in the crude oil market is investigated using a measure of the slope based on principal component analysis (PCA). The essay begins by reviewing the main theories of the relation between spot and futures prices and considering the implication of each theory on the relation between the slope of the forward curve and volatility. The diagonal VECH model of Bollerslev et al. (1988) was used to analyse the relationship between of the forward curve slope and the variances of the spot and futures prices and the covariance between them. The results show that there is a significant quadratic relationship and that exploiting this relation improves the hedging performance using futures contracts. The third essay attempts to model the spot price process of crude oil using the notion of convenience yield in a regime switching framework. Unlike the existing studies, which assume the convenience yield to have either a constant value or to have a stochastic behaviour with mean reversion to one equilibrium level, the model of this essay extends the Brennan and Schwartz (1985) model to allows for regime switching in the convenience yield along with the other parameters. In the essay, a closed form solution for the futures price is derived. The parameters are estimated using an extension to the Kalman filter proposed by Kim (1994). The regime switching one-factor model of this study does a reasonable job and the transitional probabilities play an important role in shaping the futures term structure implied by the model.

This thesis consists of three essays on risk management in crude oil markets. In the first essay, the valuation of an oil sands project is studied using real options approach. Oil sands production consumes substantial amount of natural gas during extracting and upgrading. Natural gas prices are known to be stochastic and highly volatile which introduces a risk factor that needs to be taken into account. The essay studies the impact of this risk factor on the value of an oil sands project and its optimal operation. The essay takes into account the co-movement between crude oil and natural gas markets and, accordingly, proposes two models: one incorporates a long-run link between the two markets while the other has no such link. The valuation problem is solved using the Least Square Monte Carlo (LSMC) method proposed by Longsta ff and Schwartz (2001) for valuing American options. The valuation results show that incorporating a long-run relationship between the two markets is a very crucial decision in the value of the project and in its optimal operation. The essay shows that ignoring this long-run relationship makes the optimal policy sensitive to the dynamics of natural gas prices. On the other hand, incorporating this long-run relationship makes the dynamics of natural gas price process have a very low impact on valuation and the optimal operating policy. In the second essay, the relationship between the slope of the futures term structure, or the forward curve, and volatility in the crude oil market is investigated using a measure of the slope based on principal component analysis (PCA). The essay begins by reviewing the main theories of the relation between spot and futures prices and considering the implication of each theory on the relation between the slope of the forward curve and volatility. The diagonal VECH model of Bollerslev et al. (1988) was used to analyse the relationship between of the forward curve slope and the variances of the spot and futures prices and the covariance between them. The results show that there is a significant quadratic relationship and that exploiting this relation improves the hedging performance using futures contracts. The third essay attempts to model the spot price process of crude oil using the notion of convenience yield in a regime switching framework. Unlike the existing studies, which assume the convenience yield to have either a constant value or to have a stochastic behaviour with mean reversion to one equilibrium level, the model of this essay extends the Brennan and Schwartz (1985) model to allows for regime switching in the convenience yield along with the other parameters. In the essay, a closed form solution for the futures price is derived. The parameters are estimated using an extension to the Kalman filter proposed by Kim (1994). The regime switching one-factor model of this study does a reasonable job and the transitional probabilities play an important role in shaping the futures term structure implied by the model.

Since the financial crisis of 2008, the risk awareness has increased in the -financial sector. Companies are regulated with regards to risk exposure. These regulations are driven by the Basel Committee that formulates broad supervisory standards, guidelines and recommends statements of best practice in banking supervision. In these regulations companies are regulated with own funds requirements for market risks. This thesis constructs an internal model for risk management that, according to the "Capital Requirements Regulation" (CRR) respectively the "Fundamental Review of the Trading Book" (FRTB), computes the regulatory capital requirements for market risks. The capital requirements according to CRR and FRTB are compared to show how the suggested move to an expected shortfall (ES) based model in FRTB will affect the capital requirements. All computations are performed with data that have been provided from a power trading company to make the results fit reality. In the results, when comparing the risk capital requirements according to CRR and FRTB for a power portfolio with only linear assets, it shows that the risk capital is higher using the value-at-risk (VaR) based model. This study shows that the changes in risk capital mainly depend on the different methods of calculating the risk capital according to CRR and FRTB respectively and minor on the change of risk measure. / I samband med finanskrisen 2008 har riskmedvetenheten ökat i den finansiella sektorn. Företag regleras mot riskexponering av föreskrifter som drivs av Baselkommittén, de utformar tillsynsstandarder och riktlinjer samt rekommenderar åtgärder av bästa praxis. I dessa föreskrifter regleras företag av kapitalbaskrav mot marknadsrisker. I det här examensarbetet beskrivs processen för att ta fram en intern riskmodell, enligt "Capital Requirements Regulation"(CRR) respektive Fundamental Review of the Trading Book"(FRTB), för att beräkna de lagstadgade kapitalkraven mot marknadsrisker. Kapitalbaskraven enligt regelverken jämförs för att förstå hur det föreslagna bytet till en expected shortfall (ES) baserad modell i FRTB kommer att påverka kapitalbaskraven. I alla beräkningar anv änds data från ett elhandelsföretag för att göra resultaten mer intressanta och verklighetsanpassade. I resultatdelen, vid jämförelse av riskkapitalkraven enligt CRR och FRTB för en energiportfölj med endast linjära tillgångar kan det ses att riskkapitalet blir högre med en value-at-risk (VaR) baserad modell. Den viktigaste upptäckten med detta är att skillnaden i riskkapitalkraven inte främst beror på de olika riskmåtten utan snarare de olika metoderna för att beräkna riskkapitalet enligt CRR och FRTB.

2008年初，正值美國籠罩次級房貸風暴影響、全球經濟景氣趨緩、產油國地緣政治因素造成能源價格創新高…等險峻經濟狀況之際，投資銀行設計一包含 :搭配出局條款之CMS Spread雪球型利率結構商品及結合附加WTI上限、USD/JPY匯率上下限之異型選擇權的混合結構性商品提案。本文依據標的資產屬性，參考相關文獻及近期在頂級期刊發表之利率資產評價模型研究中，選用Extended BGM模型(Ting-Pin Wu, and Son-Nan Chen(2007))、遠期曲線模型及匯率評價模型為個案之基礎評價模型；以無套利觀念依取得之市場各資產相關公開報價資料估算各模型所需之參數；由於屬於雪球利率結構型商品及路徑相關特性，在目前相關文獻無封閉解的條件下，使用蒙地卡羅模擬獲得未來各資產之現金流折現值，進而計算預期理論價值。依據上述方法論評價所獲得之預期理論價格顯示，個案並非具公平價值之交易，依此結論強烈建議客戶不應該承做本交易。 個案相當於投資銀行以買入一個5年期附帶出局條件，隱含看空經濟景氣循環之CMS Spread選擇權及買入一個1年期看空WTI價格選擇權建構此混合結構性商品。為強化客戶承做意願，設立一似乎觸及機會很大，但從交易後至今從未觸及的出局條件，又透過每日數位選擇權計息方式將WTI波動度資產化，提供大於10%之相對LIBOR rate 很高，但實際是被低估之半年收息固定費率。由於雪球型利率結構型商品特性，收益不僅取決於是否達成交易付款條件，更重要因素是達成時間點之速度。 在蒙地卡羅模擬資產價格路徑中，觸及頭一次CMS Spread付款條件天數之眾數區間為125至135，貼近實際136天。從評價結果，交易之付款條件內已隱含透過兩個不同標的資產選擇權之高預期獲利相互達到避險、套利及強化收益等效益;投資銀行可以不用額外對受眾多複雜不確定因數影響之WTI價格採取避險策略，而將所有避險成本轉嫁於選擇權賣方的客戶。在資本計提規範下及確保未來預期收益之考量下，投資銀行唯一要做是以低成本尋求中介銀行進行背對背交易以強化因市場風險所衍生之信用風險。 從研究過程，不禁讚嘆個案是投資銀行設計建構在財務工程科學上的卓越藝術及策略，從它一旦出現世界上之瞬間，個人預估其價值將達34,211,458.09美元! / Early 2008 was a steep economic era when U.S. was enveloped by subprimemortgage crisis, world's economy was slowing down, and energy prices were pushed to a historical record high by oil geopolitical factors. Under this situation, an investmentbank designed a hybrid structure product, which includes a CMS Spread Snowball interest rate structured product with USD/JPY FX rate Knock out condition, a WTIoption of an additional upper limit, a USD/JPY exchange rate combined exotic option of upper and lower limits. After considering assets attributes and reviewing the relevant literature and recent research published in top journals related to the interest rate assetpricing model, Extended BGM model (Ting-Pin Wu, and Son-Nan Chen (2007)), forward curve model, and FX Rate model are selected as the basic pricing models. Tocalculate the expected theoretical value of this structured product, the unavailable model parameters of assets are estimated through the public market data based on thearbitrage-free concept, and the discounted values of the assets future cash flows are obtained by Monte Carlo simulation because of snowball interest rate structured product and path dependency characteristic and no close form solution in current relevant literature. The results of the pricing models shows that the net present value(NPV) received by customers is lower than that received by the investment bank, theconclusion is : Strongly recommend customers should not to do this trade ! In this case, the investment bank used a long position of one 5-year period CMSSpread Option with knock out condition, which implies Bearish on the economic cycle, and a short position of a 1-year period WTI option with up and low limits condition to construct this hybrid structure product. To draw customers’ attention to this proposal, the investment bank designed a knock out condition that seemed to be met very easily,but the price never touched by the article finished date. Additionally, a daily accrued digital option is used to transfer WTI volatility to a semi-annual fixed yield over 10% that, compared to LIBOR Rate, is very high but actually is underestimated. For theSnowball structure product, the total profit depends on not only when but also, more importantly, how soon to meet the payment condition. According to the asset pricing path generated by Monte Carlo simulation, the mode range which CMS Spread payment condition first met is 125 to 135 days after the contract’s value date, very close to the actually history data of 136 days. From pricing results, terms of contract implied that two different options combined to hedge risk and gain profit from each other. Hence, the investment bank does not need to make extrahedge strategy to WTI price which is impacted by more complicated risk factors.However, customer must spend hedge cost because of taking much risk as a sell option role. Under the Capital Charge regulation, to lock up the expected profit, what the investment bank needs to do is only to pay a very low cost fee, which like insurancepremium, to look for an intermediary bank to offer a back to back trade to manage thecredit risk caused by market risk! During the research of this paper, I am amazed what an excellent art and strategy that designed by the investment bank based on financial engineering science! As this structure product appeared in this world, I estimated that it would worth 34,211,458.09 USD.

The global financial crisis of 2007 caused abrupt changes in the financial markets. Interest rates that were known to follow each other diverged. Furthermore, both regulation and an increased awareness of counterparty credit risks have fuelled a growth of collateralised contracts. As a consequence, pre-crisis swap pricing methods are no longer valid. In light of this, the purpose of this thesis is to apply a framework to the Swedish swap market that is able to consistently price interest rate and cross currency swaps in the presence of non-negligible cross currency basis spreads, and to investigate the pricing differences arising from the use and type of collat- eral. Through the implementation of a framework proposed by Fujii, Shimada and Takahashi (2010b), it is shown that the usage of collateral has a noticeable impact on the pricing. Ten year forward starting swaps are found to be priced at lower rates under collateral. Moreover, the results from pricing off-market swaps show that disregarding the impact of collateral would cause one to consistently underestimate the change in value of a contract, whether in or out of the money. The choice of collateral currency is also shown to matter, as pricing under SEK and USD as the collateral currencies yielded different results, in terms of constructed curves as well as in the pricing of spot starting, forward starting and off-market swaps. Based on the results from the pricing of off-market swaps, two scenarios are outlined that exemplify the importance of correct pricing methods when terminating and novating swaps. It is concluded that a market participant who fails to recognise the pricing implications from the usage and type of collateral could incur substantial losses. / Finanskrisens utbrott år 2007 orsakade abrupta förändringar i finansmarknaden. Räntor som tidigare följt varandra divergerade. Vidare gav både reglering av finansmarknaden och en ökad medvetenhet om motparters kreditrisk upphov till en tillväxt av kontrakt med ställda säkerheter. Följaktligen är det inte längre korrekt att prissätta swappar enligt metoder från tiden före finanskrisen. Mot bakgrund av detta är syftet med denna uppsats att applicera ett ramverk på den svenska swapmarknaden som på ett konsekvent sätt kan prissätta ränte- och valutaswappar med icke negligerbara räntespreadar, samt att undersöka prisskillnaderna som uppstår från användandet och typen av ställda säkerheter. Genom implementering av ett ramverk av Fujii, Shimada och Takahashi (2010b) visar denna studie att användandet av ställda säkerheter har en noterbar påverkan på prissättningen. Swappar med tio års löptider och framtida startdatum prissattes lägre när ställda säkerheter inkluderades i prissättningen. Vidare visar resultaten från prissättningen av off-market swappar att genom att bortse från effekten av ställda säkerheter så undervärderas ett kontrakts värdeförändring genomgående, oavsett om kontraktet är in the money eller out of the money. Valet av valuta på de ställda säkerheterna visade sig också spela roll, då prissättningen med SEK och USD som säkerhetsvalutor gav olika resultat i termer av konstruerade kurvor och i prissättning av spot-startande, framtida startande och off-market swappar. Baserat på resultaten ovan genererades två scenarion som påvisade vikten av en korrekt prissättningsmetod vid byte av motpart eller stängning av en swap. Härifrån dras slutsatsen att en marknadsaktör som inte inser vilken påverkan valet av ställda säkerheter har på prissättningen kan drabbas av betydande förluster.

[pt] O desenvolvimento de métodos simples e efetivos para estimar o valor da curva forward de energia elétrica pode permitir que participantes do mercado precifiquem adequadamente suas posições especulativas ou defensivas. Uma ferramenta como esta poderia promover maior transparência para a definição dos preços futuros permitindo que os participantes do mercado futuro possam atuar com mais segurança e trazendo com isso um necessário aumento de liquidez. Neste trabalho apresento um modelo com dois agentes representativos que administram sua exposição ao risco através de um contrato por diferenças entre o preço futuro esperado da energia elétrica na região Sudeste no Brasil e um preço de referência. Demonstra-se que este mecanismo pode abranger todos os participantes do mercado, quer sejam especuladores ou agentes envolvidos na comercialização. A função de utilidade de cada participante é modelada utilizando uma versão Generalizada da Preferência CVaR Estendida (ECP-G) e o equilíbrio nesta transação é obtido através da minimização da diferença quadrática do equivalente certo destes agentes. Os resultados obtidos são comparados às previsões de mercado feitas por especialistas para o mesmo período e demonstram aderência dentro e fora da amostra. / [en] The development of simple and effective mechanisms to estimate the value of the forward curve of power could enable market participants to better price hedging or speculative positions. This could in turn provide transparency in future price definition to all market participants and lead to more safety and liquidity in the market for electricity futures and power derivatives. This work presents a model for two market participants, a buyer and a seller of a contract for difference on the future spot price of electricity in southwest Brazil. It is shown that this model is representative of all market participants that have exposure to the future price of power. Each participant s utility function is modelled using a Generalized Extended CVaR Preference (ECP-G) and the market equilibrium is obtained through the minimization of the quadratic difference between the certainty equivalent of both agents. The results are compared with prediction of the future spot price of power made by market specialists and found to yield reasonable results when using out of sample data.